Central value of automorphic $L-$functions

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We prove a generalization to the totally real field case of the Waldspurger's formula relating the Fourier coefficient of a half integral weight form and the central value of the L-function of an integral weight form. Our proof is based on a new interpretation of Waldspurger's formula in terms of equality between global distributions. As applications we generalize the Kohnen-Zagier formula for holomorphic forms and prove the equivalence of the Ramanujan conjecture for half integral weight forms and a case of the Lindelof hypothesis for integral weight forms. We also study the Kohnen space in the adelic setting.

Keywords

Number Theory, Representation Theory, 11F70; 11F37; 11F67

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/66238

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0301115
 http://arxiv.org/abs/math/0301115

Collections

arXiv