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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

An application of the regularized
Siegel-Weil formula on unitary groups
to a theta lifting problem


Author: Victor Tan
Journal: Proc. Amer. Math. Soc. 127 (1999), 2811-2820
MSC (1991): Primary 11F70; Secondary 11F27, 22E50
Published electronically: April 23, 1999
MathSciNet review: 1641117
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $U(2)$ and $U(2,1)$ be the pair of unitary groups over a global field $F$ and $\pi$ an irreducible cuspidal representation of $U(2)$ which satisfies a certain $L$-function condition. By using a regularized Siegel-Weil formula, we can show that the global theta lifting of $\pi$ in $U(2,1)$ is non-trivial if every local factor $\pi _{\upsilon}$ of $\pi$ has a local theta lifting (Howe lifting) in $U(2,1)(F_{\upsilon})$.


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Additional Information

Victor Tan
Affiliation: Department of Mathematics, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260
Email: mattanv@nus.edu.sg

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05173-4
PII: S 0002-9939(99)05173-4
Received by editor(s): December 2, 1997
Published electronically: April 23, 1999
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 1999 American Mathematical Society