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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

   

 

Eigenfunctions of the Weil representation
of unitary groups of one variable


Author: Tonghai Yang
Journal: Trans. Amer. Math. Soc. 350 (1998), 2393-2407
MSC (1991): Primary 11F27, 11E45
MathSciNet review: 1407714
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Abstract: In this paper, we construct explicit eigenfunctions of the local Weil representation on unitary groups of one variable in the $p$-adic case when $p$ is odd. The idea is to use the lattice model, and the results will be used to compute special values of certain Hecke $L$-functions in separate papers. We also recover Moen's results on when a local theta lifting from $U(1)$ to itself does not vanish.


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Additional Information

Tonghai Yang
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: thyang@math.lsa.umich.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-98-01915-1
PII: S 0002-9947(98)01915-1
Keywords: Eigenfunction, lattice model, unitary group
Received by editor(s): November 7, 1995
Received by editor(s) in revised form: July 3, 1996
Additional Notes: Partially supported by NSF grant DMS-9304580
Article copyright: © Copyright 1998 Americal Mathematical Society