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Eigenfunctions of the Weil representation of unitary groups of one variable

Author(s): Tonghai Yang
Journal: Trans. Amer. Math. Soc. 350 (1998), 2393-2407.
MSC (1991): Primary 11F27, 11E45
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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: 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
Copyright of article: Copyright 1998, Americal Mathematical Society

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The following works have cited this article

T.H. Yang, Theta liftings and Hecke L-functions, J. reine angew. math 485 (1997), 25-53.

F. Rodriquez Villegas and T.H. Yang, Central values of Hecke L-functions of CM number fields, Duke Math. J. 98 (1999), 541-564.

yang, tonghai, nonvanishing of central Hekce L-values and rank of certain elliptic curves, Compositio Math. 117 (1999), 337-359.

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