Relative trace formulas and subconvexity estimates for $L$-functions of Hilbert modular forms
Volume 176 / 2016
Acta Arithmetica 176 (2016), 1-63
MSC: Primary 11F67; Secondary 11F72.
DOI: 10.4064/aa8021-4-2016
Published online: 10 October 2016
Abstract
We elaborate an explicit version of the relative trace formula on ${\rm PGL}(2)$ 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 on quadratic base change $L$-functions for Hilbert cusp forms with a subconvex exponent in the weight aspect.
