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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Eulerianity of Fourier coefficients of automorphic forms
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by Dmitry Gourevitch, Henrik P. A. Gustafsson, Axel Kleinschmidt, Daniel Persson and Siddhartha Sahi
Represent. Theory 25 (2021), 481-507
Published electronically: June 7, 2021


We study the question of Eulerianity (factorizability) for Fourier coefficients of automorphic forms, and we prove a general transfer theorem that allows one to deduce the Eulerianity of certain coefficients from that of another coefficient. We also establish a ‘hidden’ invariance property of Fourier coefficients. We apply these results to minimal and next-to-minimal automorphic representations, and deduce Eulerianity for a large class of Fourier and Fourier–Jacobi coefficients. In particular, we prove Eulerianity for parabolic Fourier coefficients with characters of maximal rank for a class of Eisenstein series in minimal and next-to-minimal representations of groups of ADE-type that are of interest in string theory.
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Bibliographic Information
  • Dmitry Gourevitch
  • Affiliation: Faculty of Mathematics and Computer Science, Weizmann Institute of Science, POB 26, Rehovot 76100, Israel
  • MR Author ID: 843930
  • ORCID: 0000-0001-6436-2092
  • Email:
  • Henrik P. A. Gustafsson
  • Affiliation: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540; Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854; Department of Mathematical Sciences, University of Gothenburg; and Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
  • MR Author ID: 1157059
  • ORCID: 0000-0002-3364-1547
  • Email:
  • Axel Kleinschmidt
  • Affiliation: Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Am Mühlen- berg 1, DE-14476 Potsdam, Germany; and International Solvay Institutes, ULB-Campus Plaine CP231, BE-1050, Brussels, Belgium
  • MR Author ID: 721044
  • Email:
  • Daniel Persson
  • Affiliation: Department of Mathematical Sciences, Chalmers University of Technology, SE-412 96 Gothenburg, Sweden
  • MR Author ID: 799483
  • Email:
  • Siddhartha Sahi
  • Affiliation: Department of Mathematics, Rutgers University, Hill Center - Busch Campus, 110 Frelinghuysen Road, Piscataway, New Jersey 08854-8019
  • MR Author ID: 153000
  • Email:
  • Received by editor(s): May 12, 2020
  • Received by editor(s) in revised form: October 7, 2020
  • Published electronically: June 7, 2021
  • Additional Notes: The first author was partially supported by ERC StG grant 637912 and BSF grant 2019724. The second and fourth authors were supported by the Swedish Research Council (Vetenskapsrådet), grants 2018-06774 and 2018-04760, respectively. The fifth author was partially supported by NSF grants DMS-1939600 and DMS-2001537, and Simons’ foundation grant 509766.
  • © Copyright 2021 American Mathematical Society
  • Journal: Represent. Theory 25 (2021), 481-507
  • MSC (2020): Primary 11F30, 11F70, 22E55, 20G45
  • DOI:
  • MathSciNet review: 4273169