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

Kartik Prasanna

Type: Article

Publication Date: 2006-05-01

Citations: 54

DOI: https://doi.org/10.4007/annals.2006.163.901

Abstract

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.

Locations

Annals of Mathematics - View - PDF

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