Twisted Hilbert modular L-functions and spectral theory

Abstract

These are notes for four lectures given at the 2010 CIMPA Research School "Automorphic Forms and L-functions" in Weihai, China. The lectures focused on a Burgess-like subconvex bound for twisted Hilbert modular L-functions published jointly with Valentin Blomer in the same year. They discussed the proof in some detail, especially how spectral theory can be used to estimate the relevant shifted convolution sums efficiently. They also discussed briefly an application for the number of representations by a totally positive ternary quadratic form over a totally real number field.