Integrality of a ratio of Petersson norms and level-lowering congruences
| Autor: | Kartik Prasanna |
|---|---|
| Rok vydání: | 2006 |
| Předmět: |
Pure mathematics
Mathematics::Number Theory Mathematical analysis Holomorphic function Congruence relation Petersson inner product Faltings height Mathematics (miscellaneous) Triple product Eigenform Statistics Probability and Uncertainty Mathematics::Representation Theory Finite set Eigenvalues and eigenvectors Mathematics |
| Zdroj: | Annals of Mathematics. 163:901-967 |
| ISSN: | 0003-486X |
| DOI: | 10.4007/annals.2006.163.901 |
| Popis: | We prove integrality of the ratiof, 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 con- gruences 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 integral- ity of a certain triple product L-value and the second to the computation of the Faltings height of Jacobians of Shimura curves. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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