On the first Betti numbers of hyperbolic surfaces
type: Item
instance of: scholarly article
title: On the first Betti numbers of hyperbolic surfaces
zbMATH Open document ID: 0741.22011
DOI: 10.1215/S0012-7094-91-06404-5
author: Xiaoxi Xue
published in: Duke Mathematical Journal
publication date: 1992-06-26T00:00:00Z
review text: Let \(G\) be \(SO(n,1)\) or \(SU(n,1)\) and \(\Gamma\) a cocompact, torsion-free, discrete subgroup of \(G\). Using the Selberg trace formula the author gets an upper bound of the multiplicity of the spherical complementary series \(\pi_{1,-i\alpha\rho}\), \(0<\alpha\leq 1\), of \(G\) in \(L^ 2(\Gamma\setminus G)\). From that upper bound the author estimates the first Betti numbers for \(G=SU(2,1)\).
Mathematics Subject Classification ID: 22E46
Mathematics Subject Classification ID: 11F72
Mathematics Subject Classification ID: 11F70
zbMATH DE Number: 24261
zbMATH Keywords: discrete subgroup
zbMATH Keywords: Selberg trace formula
zbMATH Keywords: multiplicity
zbMATH Keywords: spherical complementary series
zbMATH Keywords: first Betti numbers
reviewed by: Yangbo Ye
MaRDI profile type: Publication
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full work available at URL: s0012-7094-91-06404-5
OpenAlex ID: W2083071147
description: scientific article; zbMATH DE number 24261