A comparison of automorphic \(L\)-functions in a theta series lifting for unitary groups
type: Item
instance of: scholarly article
title: A comparison of automorphic \(L\)-functions in a theta series lifting for unitary groups
zbMATH Open document ID: 0972.11043
DOI: 10.1007/BF02773214
author: Takao Watanabe
published in: Israel Journal of Mathematics
publication date: 2000-09-19T00:00:00Z
review text: Let \(E/F\) be a quadratic extension of algebraic number fields. Consider the quasi-split unitary groups \(\text{U}(2n)\) and \(\text{U}(2n+1)\) over \(F\) split by \(E/F\). There is a \(\Theta\)-lifting \(\sigma\mapsto\sigma^{\ast}\) from cuspidal automorphic representations of \(\text{U}(2n)\) to automorphic representations of \(\text{U}(2n+1)\). The paper gives a relation between the partial \(L\)-functions \(L_S(s,\sigma\times\pi)\) and \(L_S(s,\sigma^{\ast}\times\pi)\), where \(\pi\) is an irreducible cuspidal automorphic representation of \(R_{E/F}\text{GL}(n)\).
Mathematics Subject Classification ID: 11F70
Mathematics Subject Classification ID: 11F66
zbMATH DE Number: 1445776
zbMATH Keywords: quasi-split unitary groups
zbMATH Keywords: \(\Theta\)-lifting
zbMATH Keywords: cuspidal automorphic representations
zbMATH Keywords: automorphic representations
zbMATH Keywords: partial \(L\)-functions
reviewed by: J. G. M. Mars
MaRDI profile type: Publication
cites work: Canonical Extensions of Harish-Chandra Modules to Representations of G
cites work: Twisted tensors and Euler products
cites work: On poles of twisted tensor \(L\)-functions
cites work: Explicit constructions of automorphic \(L\)-functions
cites work: Q3312315
cites work: \(L\)-functions and Fourier-Jacobi coefficients for the unitary group \(U(3)\)
cites work: Q4118032
cites work: Rankin-Selberg Convolutions
cites work: On Euler Products and the Classification of Automorphic Representations I
cites work: Q3470542
cites work: Q3497288
cites work: Whittaker functions for the large discrete series representations of \(\mathrm{SU}(2,1)\) and related zeta integrals
cites work: On the Ramanujan conjecture and finiteness of poles for certain \(L\)-functions
cites work: Rankin-Selberg convolutions for 𝑆𝑂_{2𝑙+1}×𝐺𝐿_{𝑛}: local theory
cites work: On \(L\)-functions and intertwining operators for unitary groups
cites work: Theta liftings for quasi-split unitary groups
cites work: Q4337521
description: scientific article; zbMATH DE number 1445776