An explicit Waldspurger formula for Hilbert modular forms

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.

16 pages

References in corpus (3)

• Explicit Gross-Zagier and Waldspurger Formulae
• Newforms in the Kohnen plus space
• Nonvanishing of twists of $L$-functions attached to Hilbert modular forms

Cited by in corpus (2)

• Effective construction of Hilbert modular forms of half-integral weight
• An explicit Waldspurger formula for Hilbert modular forms II