Plus/minus p-adic L-functions for Hilbert modular forms
SCIE
SCOPUS
- Title
- Plus/minus p-adic L-functions for Hilbert modular forms
- Authors
- Park, J; Shahab Shahabi
- Date Issued
- 2011-09-15
- Publisher
- Elsevier
- Abstract
- R. Pollack constructed in Pollack (2003) [13] plus/minus p-adic L-functions for elliptic modular forms, which are p-adically bounded, when the Hecke eigenvalues at p are zero (the most super-singular case). The goal of this work is to generalize his construction to Hilbert modular forms. We find a suitable condition for Hilbert modular forms corresponding to the vanishing of p-th Hecke eigenvalue in elliptic modular form case, which guarantees the existence of plus/minus p-adic L-functions which are p-adically bounded. As an application, we construct cyclotomic plus/minus p-adic L-functions for modular elliptic curves over a totally real field F under the assumption that a(p)(E) = 0 for each prime p dividing p. We formulate a cyclotomic plus/minus Iwasawa main conjecture for such elliptic curves. (C) 2011 Elsevier Inc. All rights reserved.
- Keywords
- Hilbert modular forms; p-Adic L-functions at supersingular primes; Selmer groups; Elliptic curves; SUPERSINGULAR PRIMES; ELLIPTIC-CURVES; IWASAWA THEORY; ZETA-FUNCTIONS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/17287
- DOI
- 10.1016/J.JALGEBRA.2011.04.033
- ISSN
- 0021-8693
- Article Type
- Article
- Citation
- JOURNAL OF ALGEBRA, vol. 342, no. 1, page. 197 - 211, 2011-09-15
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