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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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Distinguished representations and quadratic base change for $GL(3)$
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by Herve Jacquet and Yangbo Ye PDF
Trans. Amer. Math. Soc. 348 (1996), 913-939 Request permission

Abstract:

Let $E/F$ be a quadratic extension of number fields. Suppose that every real place of $F$ splits in $E$ and let $H$ be the unitary group in 3 variables. Suppose that $\Pi$ is an automorphic cuspidal representation of $GL(3,E_{\mathbb {A}})$. We prove that there is a form $\phi$ in the space of $\Pi$ such that the integral of $\phi$ over $H(F)\setminus H(F_{\mathbb {A}})$ is non zero. Our proof is based on earlier results and the notion, discussed in this paper, of Shalika germs for certain Kloosterman integrals.
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Additional Information
  • Herve Jacquet
  • Affiliation: Department of Mathematics, Columbia University, New York, New York 10027
  • Email: hj@math.columbia.edu
  • Yangbo Ye
  • Affiliation: Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
  • MR Author ID: 261621
  • Email: yey@math.uiowa.edu
  • Received by editor(s): November 20, 1994
  • Additional Notes: Partially supported by NSF grant DMS-91-01637
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 913-939
  • MSC (1991): Primary 11F70, 11R39; Secondary 22E50
  • DOI: https://doi.org/10.1090/S0002-9947-96-01549-8
  • MathSciNet review: 1340178