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A nonabelian trace formula

Research in the Mathematical Sciences20152:14

  • Received: 18 November 2014
  • Accepted: 31 March 2015
  • Published:


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


  • Base Change
  • Haar Measure
  • Fundamental Domain
  • Trace Formula
  • Automorphic Form