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

Xue, Hui

doi:10.1090/S0002-9939-2010-10660-3

Central values of $L$-functions and half-integral weight forms
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Proc. Amer. Math. Soc. 139 (2011), 21-30 Request permission

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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