English

An explicit Waldspurger formula for Hilbert modular forms

Number Theory 2018-07-13 v2

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.

Keywords

Cite

@article{arxiv.1603.03753,
  title  = {An explicit Waldspurger formula for Hilbert modular forms},
  author = {Nicolás Sirolli and Gonzalo Tornaría},
  journal= {arXiv preprint arXiv:1603.03753},
  year   = {2018}
}

Comments

16 pages

R2 v1 2026-06-22T13:09:07.329Z