A Remark on Whittaker Functions on $Sp(2,\Bbb R)$

J. Math. Sci. Univ. Tokyo
Vol. 9 (2002), No. 4, Page 627--635.

Moriyama, Tomonori
A Remark on Whittaker Functions on $Sp(2,\Bbb R)$
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Let $π$ be a principal series representation of $G=Sp(2,\Bbb R)$ induced from the maximal parabolic subgroup of $G$ with non-abelian unipotent radical. We show that Whittaker functions on $G$ corresponding to a certain $K$-finite vector of $π$ have simple integral expressions of Mellin-Barnes type. As an application, we compute the real component of Novodvorsky's zeta integral for $GSp(2) × GL(2)$ in a special case.

Mathematics Subject Classification (1991): Primary 22E50; Secondary 11F70, 22E45
Mathematical Reviews Number: MR1947484

Received: 2000-12-14