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

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.

57 pages, minor changes made to version 1. The final version of this article will be published in the Duke Mathematical Journal, Vol. 149, No. 2, published by Duke University Press