Central Value Of Automorphic <Emphasis Type="Italic">L</Emphasis>-Functions |
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Authors: | Ehud Moshe Baruch Zhengyu Mao |
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Institution: | (1) Department of Mathematics, Technion, Haifa, 32000, Israel;(2) Department of Mathematics and Computer Science, Rutgers University, Newark, NJ 07102-1811, USA |
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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 as a combination
of two ingredients – an equality between global distributions, and a dichotomy result for theta correspondence. 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 Lindel?f hypothesis for integral weight forms. We also study the Kohnen space in the
adelic setting.
The first author was partially supported by NSF grant DMS-0070762. The second author was partially supported by NSF grant
DMS-0355285.
Received: July 2005 Accepted: August 2005 |
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Keywords: | Waldspurger correspondence half integral weight forms special values of L-functions |
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