An explicit Waldspurger formula for Hilbert modular forms

Sirolli, Nicolás; Tornaría, Gonzalo

doi:10.1090/tran/7112

An explicit Waldspurger formula for Hilbert modular forms
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by Nicolás Sirolli and Gonzalo Tornaría PDF

Trans. Amer. Math. Soc. 370 (2018), 6153-6168

Abstract:

We describe a construction of preimages for the Shimura map on Hilbert modular forms and give an explicit Waldspurger type formula relating their Fourier coefficients to central values of twisted $L$-functions. Our construction is inspired by that of Gross and applies to any nontrivial level and arbitrary base field, subject to certain conditions on the Atkin-Lehner eigenvalues and on the weight.

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