The exponent of convergence of Poincaré series associated with some discontinuous groups
type: Item
instance of: scholarly article
title: The exponent of convergence of Poincaré series associated with some discontinuous groups
zbMATH Open document ID: 0662.30041
author: Masami Nakada
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1988-01-01T00:00:00Z
review text: The following theorem is proved. Suppose \(\Gamma\) is a discontinuous group of conformal motions of the \((n+1)\)-dimensional ball \(B^{n+1}\) and assume that the limit set \(\Lambda\) (\(\Gamma)\) has more than two points. Further assume \(\xi_ 0\in \Lambda (\Gamma)\) is a parabolic fixed point, that is, \(\xi_ 0\) is the only fixed point of some \(\gamma\in \Gamma\) and that the isotropy group of \(\xi_ 0\) has a rank k free abelian subgroup. Then the exponent of convergence of \(\Gamma\) is at least k and this estimate is best possible.
Mathematics Subject Classification ID: 30F35
zbMATH DE Number: 4081931
zbMATH Keywords: Poincaré series
zbMATH Keywords: hyperbolic groups
zbMATH Keywords: exponent of convergence
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178227983
OpenAlex ID: W2038880832
cites work: Q3665386
cites work: The Exponent of Convergence of Poincaré Series
cites work: The Hausdorff dimension of the limit set of a geometrically finite Kleinian group
DOI: 10.2748/TMJ/1178227983
description: scientific article; zbMATH DE number 4081931