Integrality of a ratio of Petersson norms and level-lowering congruences

• 成果类型: Article
• 署名作者: Prasanna, Kartik
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2006.163.901
• 发表日期: 2006
• 页码: 901-967
• 关键词: imaginary quadratic fields; totally-real fields; modular-forms; zeta-functions; automorphic-forms; special values; adic representations; dirichlet series; elliptic-curves; cusp forms

摘要

We prove integrality of the ratio < f, f >/(g, g) (outside an explicit finite set of primes), where g is an arithmetically normalized holomorphic newform on a Shimura curve, f is a normalized Hecke eigenform on GL(2) with the same Hecke eigenvalues as g and <,> denotes the Petersson inner product. The primes dividing this ratio are shown to be closely related to certain level-lowering congruences satisfied by f and to the central values of a family of Rankin-Selberg L-functions. Finally we give two applications, the first to proving the integrality of a certain triple product L-value and the second to the computation of the Faltings height of Jacobians of Shimura curves.