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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the degree five $L$-function for $\mathrm {GSp}(4)$
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by Daniel File PDF
Trans. Amer. Math. Soc. 365 (2013), 6471-6497 Request permission

Abstract:

We give a new integral representation for the degree five (standard) $L$-function for automorphic representations of $\mathrm {GSp}(4)$ that is a refinement of an integral representation of Piatetski-Shapiro and Rallis. The new integral representation unfolds to produce the Bessel model for $\mathrm {GSp}(4)$ which is a unique model. The local unramified calculation uses an explicit formula for the Bessel model and differs completely from that of Piatetski-Shapiro and Rallis.
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Additional Information
  • Daniel File
  • Affiliation: Department of Mathematics, 14 MacLean Hall, University of Iowa, Iowa City, Iowa 52242-1419
  • Email: daniel-file@uiowa.edu
  • Received by editor(s): February 28, 2012
  • Received by editor(s) in revised form: April 6, 2012, and May 2, 2012
  • Published electronically: March 5, 2013
  • Additional Notes: This work was done while the author was a graduate student at Ohio State University as part of his Ph.D. dissertation
  • © Copyright 2013 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 365 (2013), 6471-6497
  • MSC (2010): Primary 11F66, 11F70
  • DOI: https://doi.org/10.1090/S0002-9947-2013-05869-2
  • MathSciNet review: 3105759