Nicolás Sirolli, Gonzalo Tornaría
Published 2018-12-30Version 1
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.
Effective construction of Hilbert modular forms of half-integral weight
Periods of Hilbert Modular forms, Kronecker series and Cohomology
Equidistribution of signs for Hilbert modular forms of half-integral weight
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