Abstract: Jointly with Valentin Blomer we proved a subconvex bound for twisted Hilbert modular L-functions which can be regarded as the analogue of Burgess' classical result for Dirichlet L-functions. I will discuss the proof in some detail, especially how spectral theory can be used to estimate the relevant shifted convolution sums efficiently. I will also discuss briefly an application for the number of representations by a positive ternary quadratic form over a totally real number field.

Lecture Notes: Twisted Hilbert modular L-functions and spectral theory