Preimages for the Shimura map on Hilbert modular forms

Abstract

In this article we give a method to construct preimages for the Shimura correspondence on Hilbert modular forms of odd and square-free level. The method relies in the ideas presented for the rational case by Pacetti and Tornaría, and is such that the Fourier coefficients of the preimages constructed can be computed explicitly.

Minor revision

References in corpus (3)

• Shimura correspondence for level $p^2$ and the central values of $L$-series II
• Computing ideal classes representatives in quaternion algebras
• Shimura correspondence for level p^2 and the central values of L-series

Cited by in corpus (2)

• An explicit Waldspurger formula for Hilbert modular forms
• An explicit Waldspurger formula for Hilbert modular forms II