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arXiv · 1812.11635

An explicit Waldspurger formula for Hilbert modular forms II

Nicolás Sirolli·Gonzalo Tornaría
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Abstract

We describe a construction of preimages for the Shimura map on Hilbert modular forms using generalized theta series, and give an explicit Waldspurger type formula relating their Fourier coefficients to central values of twisted $L$-functions. This formula extends our previous work, allowing to compute these central values when the main central value vanishes.

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Nicolás Sirolli, Gonzalo Tornaría. 2020-07-30. An explicit Waldspurger formula for Hilbert modular forms II. https://doi.org/10.1007/s11139-020-00280-z

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