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Transactions of the American Mathematical Society

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



On the degree five $L$-function for $\mathrm {GSp}(4)$

Author: Daniel File
Journal: Trans. Amer. Math. Soc. 365 (2013), 6471-6497
MSC (2010): Primary 11F66, 11F70
Published electronically: March 5, 2013
MathSciNet review: 3105759
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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

Keywords: $L$-function, integral representation, Bessel models
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
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.