Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Central values of $ L$-functions and half-integral weight forms

Author: Hui Xue
Journal: Proc. Amer. Math. Soc. 139 (2011), 21-30
MSC (2010): Primary 11F67, 11F37
Published electronically: August 26, 2010
MathSciNet review: 2729067
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Abstract: We prove a relation between the Fourier coefficients of certain Hilbert modular forms of half-integral weight and central values of the corresponding Rankin $ L$-functions. The result generalizes the classical theorem by Waldspurger. The approach is geometric and generalizes that of Gross and Hatcher.

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Hui Xue
Affiliation: Department of Mathematical Sciences, Clemson University, Clemson, South Carolina 29634

Received by editor(s): January 12, 2010
Published electronically: August 26, 2010
Communicated by: Ken Ono
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.