Eigenfunctions of the Weil representation of unitary groups of one variable

Yang, Tonghai

doi:10.1090/S0002-9947-98-01915-1

Eigenfunctions of the Weil representation of unitary groups of one variable
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by Tonghai Yang PDF

Trans. Amer. Math. Soc. 350 (1998), 2393-2407

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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