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

• Autores: Kartik Prasanna
• Localización: Annals of mathematics, ISSN 0003-486X, Vol. 163, Nº 3, 2006, págs. 901-967
• Idioma: inglés
• DOI: 10.4007/annals.2006.163.901
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• Resumen

  • 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.