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