## Illinois Journal of Mathematics

### On quasiconformal invariance of convergence and divergence types for Fuchsian groups

Katsuhiko Matsuzaki

#### Abstract

We characterize convergence and divergence types for Fuchsian groups in terms of the critical exponent of convergence and modified functions of the Poincaré series for certain subgroups associated with ends of the quotient Riemann surfaces. As an application of this result, we prove that convergence and divergence type are not invariant under a quasiconformal automorphism of the unit disk.

#### Article information

Source
Illinois J. Math., Volume 52, Number 4 (2008), 1249-1258.

Dates
First available in Project Euclid: 18 November 2009

https://projecteuclid.org/euclid.ijm/1258554360

Digital Object Identifier
doi:10.1215/ijm/1258554360

Mathematical Reviews number (MathSciNet)
MR2595765

Zentralblatt MATH identifier
1189.30081

#### Citation

Matsuzaki, Katsuhiko. On quasiconformal invariance of convergence and divergence types for Fuchsian groups. Illinois J. Math. 52 (2008), no. 4, 1249--1258. doi:10.1215/ijm/1258554360. https://projecteuclid.org/euclid.ijm/1258554360

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