Twisted L-functions over number fields and Hilbert's eleventh problem

TL;DR

This paper establishes a subconvex bound for twisted L-functions over totally real number fields, advancing understanding of automorphic forms and L-functions with novel spectral and analytical techniques.

Contribution

It introduces a Burgess-like subconvex bound for twisted L-functions over number fields using spectral decomposition and a generalized Kuznetsov formula.

Findings

Proves a subconvexity bound for twisted L-functions over totally real fields.

Develops a spectral decomposition approach for shifted convolution sums.

Utilizes a generalized Kuznetsov formula to achieve the main result.

Abstract

We prove a Burgess-like subconvex bound for twisted L-functions of a fixed irreducible cuspidal automorphic representation of GL(2) over a totally real number field. The proof is based on a spectral decomposition of shifted convolution sums and a generalized Kuznetsov formula.