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Transactions of the American Mathematical Society

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



Distinguished representations and quadratic base change for $GL(3)$

Authors: Herve Jacquet and Yangbo Ye
Journal: Trans. Amer. Math. Soc. 348 (1996), 913-939
MSC (1991): Primary 11F70, 11R39; Secondary 22E50
MathSciNet review: 1340178
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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

Yangbo Ye
Affiliation: Department of Mathematics, The University of Iowa, Iowa City, Iowa 52242
MR Author ID: 261621

Received by editor(s): November 20, 1994
Additional Notes: Partially supported by NSF grant DMS-91-01637
Article copyright: © Copyright 1996 American Mathematical Society