Certain Rankin-Selberg integral for unitary groups

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.