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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.


On the Fourier inversion formula for the full modular group
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by Keith R. Ouellette
Represent. Theory 15 (2011), 112-125
Published electronically: February 7, 2011


We offer a new proof of the Fourier inversion and Plancherel formulae for Maass-Eisenstein wave packets. The proof uses truncation, basic analysis, and classical Fourier theory. Brief sketches of the proofs due to Langlands, Lapid, and Casselman are then presented for comparison.
  • James G. Arthur, A (very brief) history of the trace formula, A note on, 2007.
  • Armand Borel, Automorphic forms on $\textrm {SL}_2(\textbf {R})$, Cambridge Tracts in Mathematics, vol. 130, Cambridge University Press, Cambridge, 1997. MR 1482800, DOI 10.1017/CBO9780511896064
  • Robert S. Doran, Ze-Li Dou, and George T. Gilbert (eds.), Automorphic forms, automorphic representations, and arithmetic, Proceedings of Symposia in Pure Mathematics, vol. 66, American Mathematical Society, Providence, RI, 1999. MR 1703754, DOI 10.1090/pspum/066.2
  • Gerald B. Folland, Real analysis, 2nd ed., Pure and Applied Mathematics (New York), John Wiley & Sons, Inc., New York, 1999. Modern techniques and their applications; A Wiley-Interscience Publication. MR 1681462
  • Tomio Kubota, Elementary theory of Eisenstein series, Kodansha, Ltd., Tokyo; Halsted Press [John Wiley & Sons, Inc.], New York-London-Sydney, 1973. MR 0429749
  • R. P. Langlands, Eisenstein series, Algebraic Groups and Discontinuous Subgroups (Proc. Sympos. Pure Math., Boulder, Colo., 1965) Amer. Math. Soc., Providence, R.I., 1966, pp. 235–252. MR 0249539
  • Erez Lapid, On Arthur’s asymptotic inner product formula of truncated Eisenstein series, to appear in Clay Mathematics Proceedings.
  • Hans Maass, Über eine neue Art von nichtanalytischen automorphen Funktionen und die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann. 121 (1949), 141–183 (German). MR 31519, DOI 10.1007/BF01329622
  • Colette Mœglin and Jean-Loup Waldspurger, Décomposition spectrale et séries d’Eisenstein, Progress in Mathematics, vol. 113, Birkhäuser Verlag, Basel, 1994 (French, with English summary). Une paraphrase de l’Écriture. [A paraphrase of Scripture]. MR 1261867
  • W. Roelcke, Analytische Fortsetzung der Eisensteinreihen zu den parabolischen Spitzen von Grenzkreisgruppen erster Art, Math. Ann. 132 (1956), 121–129 (German). MR 82562, DOI 10.1007/BF01452322
  • Walter Rudin, Functional analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. MR 0365062
  • A. Selberg, Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series, J. Indian Math. Soc. (N.S.) 20 (1956), 47–87. MR 88511
  • Atle Selberg, Discontinuous groups and harmonic analysis, Proc. Internat. Congr. Mathematicians (Stockholm, 1962) Inst. Mittag-Leffler, Djursholm, 1963, pp. 177–189. MR 0176097
  • V. S. Varadarajan, An introduction to harmonic analysis on semisimple Lie groups, Cambridge Studies in Advanced Mathematics, vol. 16, Cambridge University Press, Cambridge, 1999. Corrected reprint of the 1989 original. MR 1725738
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Bibliographic Information
  • Keith R. Ouellette
  • Affiliation: Department of Mathematics, College of the Holy Cross, Worcester, Massachusetts 01610
  • Email:
  • Received by editor(s): October 21, 2006
  • Received by editor(s) in revised form: December 10, 2010
  • Published electronically: February 7, 2011
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 15 (2011), 112-125
  • MSC (2010): Primary 22E45; Secondary 11F72
  • DOI:
  • MathSciNet review: 2772585