Averages of central L-values of Hilbert modular forms with an application to subconvexity

TL;DR

This paper derives exact formulas for averaged central L-values of Hilbert modular forms using the relative trace formula, and applies these results to address subconvexity and equidistribution problems in number theory.

Contribution

It introduces a novel application of the relative trace formula to compute averaged central L-values and uses these to study subconvexity bounds and Hecke eigenvalue distributions.

Findings

Exact formulas for averaged central L-values obtained

Subconvexity bounds for these L-functions established

Equidistribution of Hecke eigenvalues weighted by L-values proven

Abstract

We use the relative trace formula to obtain exact formulas for central values of certain twisted quadratic base change L-functions averaged over Hilbert modular forms of a fixed weight and level. We apply these formulas to the subconvexity problem for these L-functions. We also establish an equidistribution result for the Hecke eigenvalues weighted by these L-values.