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Central value of automorphic $L-$functions

Ehud Moshe Baruch·Zhengyu Mao
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Abstract

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.

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Ehud Moshe Baruch, Zhengyu Mao. 2003-01-11. Central value of automorphic $L-$functions. https://arxiv.org/abs/math/0301115

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