Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


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
Email: yey@math.uiowa.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-96-01549-8
PII: S 0002-9947(96)01549-8
Received by editor(s): November 20, 1994
Additional Notes: Partially supported by NSF grant DMS-91-01637
Article copyright: © Copyright 1996 American Mathematical Society