Tohoku Mathematical Journal

Certain Rankin-Selberg integral for unitary groups

Masao Tsuzuki

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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.

Article information

Source
Tohoku Math. J. (2), Volume 61, Number 1 (2009), 115-164.

Dates
First available in Project Euclid: 3 April 2009

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1238764549

Digital Object Identifier
doi:10.2748/tmj/1238764549

Mathematical Reviews number (MathSciNet)
MR2501865

Zentralblatt MATH identifier
1235.11047

Subjects
Primary: 11F67: Special values of automorphic $L$-series, periods of modular forms, cohomology, modular symbols
Secondary: 11F55: Other groups and their modular and automorphic forms (several variables)

Citation

Tsuzuki, Masao. Certain Rankin-Selberg integral for unitary groups. Tohoku Math. J. (2) 61 (2009), no. 1, 115--164. doi:10.2748/tmj/1238764549. https://projecteuclid.org/euclid.tmj/1238764549


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