Tohoku Mathematical Journal
2009
March
SECOND SERIES VOL. 61, NO. 1

Tohoku Math. J.
61 (2009), 115-164

Title CERTAIN RANKIN-SELBERG INTEGRAL FOR UNITARY GROUPS

Author Masao Tsuzuki

(Received May 8, 2006, revised July 17, 2008)
Abstract. We consider the real rank one unitary group $G$ and its subgroup $H$ obtained as the stabilizer of an anisotropic vector in the skew-hermitian space defining $G$. We compute the inner-product of an Eisenstein series on $H$ and a non-holomorphic cuspidal Hecke eigenform on $G$ restricted to $H$ to obtain an integral representation of the standard $L$-function of the eigenform. We also discuss some consequences of the integral representation.

2000 Mathematics Subject Classification. Primary 11F67; Secondary 11F55.

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