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CHOIE, YOUNG JU (최영주)

Dept of Mathematics(수학과)

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II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||II CODES:8||MODULARFORMS:7||SERIES:6||CUSP FORMS:6||JACOBI FORMS:6||Jacobi forms:5||selfdual codes:4||RINGS:4||HEAT OPERATOR:4||Jacobi form:4||modular forms:3||Period:3||AUTOMORPHICFORMS:3||VALUES:3||RankinCohen brackets:3||CODES:3||Z(2M):3||CONGRUENCES:3||OPERATORS:3||unimodular lattices:3||VARIETIES:3||Modular forms:2||pseudodifferential operators:2||FORMS:2||theta series:2||weight enumerator:2||congruences:2||Dirichlet series:2||Hecke operator:2||Siegel modular form:2||SiegelEisenstein series:2||LATTICES:2||totally real field:2||Eichler integral:2||Jacobilike forms:2||modular form:2||JACOBI:2||Ramanujan bound:1||Hilbert Modular form:1||codes over rings:1||Automorphic integral:1||Hyperbolic series:1||Witt operator:1||RANKS:1||cryptography:1||ternary codes:1||hyperelliptic curve cryptosystem:1||CRITICALVALUES:1||WEIGHT:1||DIVISOR CLASS GROUP:1||scalar multiplication:1||Jacobi forms over the totally real fields:1||bilinear pairing:1||Heat operator:1||NUMBERS:1||EVEN UNIMODULAR LATTICES:1||PROPERTY:1||representations:1||Jacobi forms Hilbert modular forms:1||SELFDUAL CODES:1||hyperelliptic curves:1||invariant space:1||Galois ring:1||Petersson norm:1||Frobenius map:1||CRYPTOSYSTEMS:1||SIMPLE PROOF:1||MODULAR LATTICES:1||Clifford group:1||key agreement protocol:1||Hermitian modular forms:1||Mock Jacobi form:1||polynomial ring:1||nonholomorphic Poincare series:1||MODULAR FORMS:1||nonholomorphic Eisenstein series:1||nonpordinary:1||newform:1||THETAFUNCTIONS:1||Mock modular forms:1||Mock Jacobi forms:1||HILBERT MODULARFORMS:1||elliptic curves:1||Tate pairing implementation:1||hyperelliptic cryptosystem:1||Lfunctions:1||genus theta series:1||Nonholomorphic theta function:1||halfintegral weight form:1||invariants:1||codes:1||HilbertSiegel modular forms over Q(root 5):1||Cusp forms:1||Harmonic Maass forms:1||F(Q):1||type II codes:1||Ikeda lift:1||type II code over Z(2m):1||HALFINTEGRAL WEIGHT:1||SEPTIC BASE:1||MODULAR IDENTITY:1||Ozeki polynomial:1||identitybased encryption:1||Quasimodular forms:1||QUASIMODULAR FORMS:1||SchrdingerWeil representation:1||Jacobi Hilbert modular form:1||Jacobi and Siegel forms:1||NUMBERFIELDS:1||LINEAR RELATIONS:1||GENUS:1||congruence modulo p:1||LEVEL APPELL FUNCTIONS:1||isomorphism classes:1||a generalized CliffordWeil group:1||elliptic curve cryptosystem:1||shadows:1||SMALL FIELDS:1||noncritical values:1||Hecke operators:1||Indefinite form:1||FINITE RINGS:1||CRYPTOGRAPHY:1||SIEGEL MODULARFORMS:1||Eisenstein space:1||ternary forms:1||linear relations:1||Fourier expansion:1||Lerch sum:1||EISENSTEIN SERIES:1||Mellin transformation:1||Sturm formula:1||representatives:1||invariant polynomial ring:1||ZETAFUNCTIONS:1||PI:1||code:1||QUADRATICFORMS:1||Siegel theta series:1||Fourier coefficient:1||cusp form:1||MAASS WAVEFORMS:1||GAMMA(0)(N):1||COHOMOLOGY:1||Z):1||Ozeki and BroueEnguehard maps:1||integral lattices:1||BORCHERDS PRODUCTS:1||COEFFICIENTS:1||TRACES:1||finite fields:1||DISCRETE LOGARITHM:1||ALGORITHM:1||mixed Siegel modular form:1||CONSTRUCTION:1||periods:1||1cocycles:1||DERIVATIVES:1||EIGENVALUES:1||Genus:1||

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