Central values of $L$-functions and half-integral weight forms
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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.References
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Additional Information
- Hui Xue
- Affiliation: Department of Mathematical Sciences, Clemson University, Clemson, South Caro- lina 29634
- Email: huixue@clemson.edu
- Received by editor(s): January 12, 2010
- Published electronically: August 26, 2010
- Communicated by: Ken Ono
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 21-30
- MSC (2010): Primary 11F67, 11F37
- DOI: https://doi.org/10.1090/S0002-9939-2010-10660-3
- MathSciNet review: 2729067