An explicit Waldspurger formula for Hilbert modular forms

Abstract: Computing central values of $L$-functions attached to modular forms is interesting because of the arithmetic information they encode. These values are related to Fourier coefficients of half-integral weight modular forms and the Shimura correspondence, as shown in great generality by Waldspurger.

When $g$ is a classical modular form of odd square-free level, a theorem of Baruch and Mao shows the existence of a finite set of modular forms of half-integral weight, together with an explicit formula for twisted central values $L(1/2,g,D)$ for every fundamental discriminant $D$.

In this talk I will present a generalization of this result to all levels except perfect squares, and to Hilbert modular forms over an arbitrary totally real number field.

Joint work with Nicolás Sirolli (Universidad de Buenos Aires).

number theoryrepresentation theory

Audience: researchers in the topic

Number Theory and Representations in Valparaiso