Open Access

A nonabelian trace formula

Research in the Mathematical Sciences20152:14

DOI: 10.1186/s40687-015-0025-x

Received: 18 November 2014

Accepted: 31 March 2015

Published: 3 August 2015


Let E/F be an everywhere unramified extension of number fields with Gal(E/F) simple and nonabelian. In a recent paper, the first named author suggested an approach to nonsolvable base change and descent of automorphic representations of GL2 along such an extension. Motivated by this, we prove a trace formula whose spectral side is a weighted sum over cuspidal automorphic representations of \(\text {GL}_{2}(\mathbb {A}_{E})\) that are isomorphic to their Gal(E/F)-conjugates. The basic method, which is of interest in itself, is to use functions in a space isolated by Finis, Lapid, and Müller to build more variables into the trace formula.

2010 Mathematics subject classification: Primary 11F70, Secondary 11F66