Relative trace formulas and subconvexity estimates of L-functions for Hilbert modular forms

Abstract

We elaborate an explicit version of the relative trace formula on $\PGL(2)$ over a totally real number field for the toral periods of Hilbert cusp forms along the diagonal split torus. As an application, we prove (i) a spectral equidistribution result in the level aspect for Satake parameters of holomorphic Hilbert cusp forms weighted by central $L$-values, and (ii) a bound of quadratic base change $L$-functions for Hilbert cusp forms with a subconvex exponent in the weight aspect.

This is a revised version of our previous submission

References in corpus (2)

• The subconvexity problem for $\GL_{2}$
• Existence of Hilbert cusp forms with non-vanishing $L$-values