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On the nonvanishing of the central value of the Rankin-Selberg $L$-functions


Authors: David Ginzburg, Dihua Jiang and Stephen Rallis
Journal: J. Amer. Math. Soc. 17 (2004), 679-722
MSC (2000): Primary 11F67, 11F70, 22E46, 22E55
DOI: https://doi.org/10.1090/S0894-0347-04-00455-2
Published electronically: April 1, 2004
MathSciNet review: 2053953
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Abstract: We characterize the nonvanishing of the central value of the Rankin-Selberg $L$-functions in terms of periods of Fourier-Jacobi type. This characterization is based on the Langlands philosophy on functoriality and on applications of invariant theory to automorphic representations. The result is the symplectic analog of the Gross-Prasad conjecture.


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Additional Information

David Ginzburg
Affiliation: School of Mathematical Sciences, Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat-Aviv, 69978 Israel
Email: ginzburg@post.tau.ac.il

Dihua Jiang
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: dhjiang@math.umn.edu

Stephen Rallis
Affiliation: Department of Mathematics, The Ohio State University, Columbus, Ohio 43210
Email: haar@math.ohio-state.edu

DOI: https://doi.org/10.1090/S0894-0347-04-00455-2
Keywords: Special value, $L$-function, period, automorphic form
Received by editor(s): May 8, 2003
Published electronically: April 1, 2004
Additional Notes: The second author is partially supported by the NSF grant DMS-0098003, the Sloan Research Fellowship, and the McKnight Land-Grant Professorship (University of Minnesota).
Dedicated: Dedicated to Ilya I. Piatetski-Shapiro with admiration on the occasion of his 75th birthday
Article copyright: © Copyright 2004 American Mathematical Society

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