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arXiv · 1603.03753

An explicit Waldspurger formula for Hilbert modular forms

Nicolás Sirolli·Gonzalo Tornaría
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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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Nicolás Sirolli, Gonzalo Tornaría. 2016-03-11. An explicit Waldspurger formula for Hilbert modular forms. https://doi.org/10.1090/tran%2F7112

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