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Journal of the American Mathematical Society

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

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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On the nonvanishing of the central value of the Rankin-Selberg $L$-functions
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by David Ginzburg, Dihua Jiang and Stephen Rallis PDF
J. Amer. Math. Soc. 17 (2004), 679-722 Request permission

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
  • MR Author ID: 260974
  • Email: dhjiang@math.umn.edu
  • Stephen Rallis
  • Affiliation: Department of Mathematics, The Ohio State University, Columbus, Ohio 43210
  • Email: haar@math.ohio-state.edu
  • 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
  • © Copyright 2004 American Mathematical Society
  • 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
  • MathSciNet review: 2053953