Central value of automorphic $L-$functions
数论
2007-05-23 v1 表示论
摘要
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.
引用
@article{arxiv.math/0301115,
title = {Central value of automorphic $L-$functions},
author = {Ehud Moshe Baruch and Zhengyu Mao},
journal= {arXiv preprint arXiv:math/0301115},
year = {2007}
}