Skip to Main Content

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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Distinguished representations and quadratic base change for $GL(3)$
HTML articles powered by AMS MathViewer

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.
References
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC (1991): 11F70, 11R39, 22E50
  • Retrieve articles in all journals with MSC (1991): 11F70, 11R39, 22E50
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