p-adic family of half-integral weight modular forms via overconvergent Shintani lifting
SCIE
SCOPUS
- Title
- p-adic family of half-integral weight modular forms via overconvergent Shintani lifting
- Authors
- Park, J
- Date Issued
- 2010-03
- Publisher
- Springer-Verlag
- Abstract
- The classical Shintani map (Shintani, Nagoya Math J 58:83-126, 1975) is the Hecke-equivariant map from the space of cusp forms of integral weight to the space of cusp forms of half-integral weight. In this paper, we will construct a p-adic Hecke-equivariant overconvergent Shintani lifting, for finite slope overconvergent modular forms (Coleman family), which interpolates the classical Shintani lifting p-adically, generalizing the result of G. Stevens in the case of slope 0 modular forms (Hida family) in (Stevens, Contemporary Mathematics, vol 174, 1994) (see the Theorems 3.9 and 3.11). In consequence, we get a formal q-expansion I similar to whose q-coefficients are in an overconvergent distribution ring, which can be thought of p-adic analytic family of overconvergent modular forms of half-integral weight, since the specializations of I similar to at the arithmetic weights are the classical cusp forms of half-integral weight (see the Theorem 4.20). Also the explicit description of Hecke operators on I similar to will be given.
- Keywords
- VALUES
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/25127
- DOI
- 10.1007/S00229-009-0323-Y
- ISSN
- 0025-2611
- Article Type
- Article
- Citation
- MANUSCRIPTA MATHEMATICA, vol. 131, no. 3-4, page. 355 - 384, 2010-03
- Files in This Item:
- There are no files associated with this item.
Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.