Illinois Journal of Mathematics

On quasiconformal invariance of convergence and divergence types for Fuchsian groups

Katsuhiko Matsuzaki

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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.

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

First available in Project Euclid: 18 November 2009

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Primary: 30F35: Fuchsian groups and automorphic functions [See also 11Fxx, 20H10, 22E40, 32Gxx, 32Nxx] 37F30: Quasiconformal methods and Teichmüller theory; Fuchsian and Kleinian groups as dynamical systems 37F35: Conformal densities and Hausdorff dimension


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.

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