A nonabelian trace formula

  • Jayce Robert Getz
  • Paul Edward Herman
Open Access


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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors thank R. Langlands, B. C. Ngô, and P. Sarnak for their generous help and encouragement over the past few years, and E. Lapid for pointing out a mistake in an earlier version of this paper that lead to the simpler approach exposed here. The first author also thanks H. Hahn for her constant encouragement and help with proofreading. Finally, the authors thank the referees for useful comments and corrections which improved the exposition.

The first author is thankful for partial support provided by NSF grant DMS-1405708. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation.


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Copyright information

© Getz and Herman. 2015

This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Authors and Affiliations

  1. 1.Department of MathematicsDuke UniversityDurhamUSA
  2. 2.Department of MathematicsUniversity of ChicagoChicagoUSA

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