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Meromorphic extension of the Selberg zeta function for Kleinian groups via thermodynamic formalism

Published online by Cambridge University Press:  24 October 2008

André Rocha
André Rocha
Affiliation:
Departamento de Matemática. CCEN, Universidade Federal de Pernambuco Av. Professor Luiz Freire s/n, CEP: 50670-901, Recife-PE, Brazil
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Abstract

We prove the existence of a piecewise analytic expanding map associated to certain Kleinian groups without parabolics acting in the 3-dimensional hyperbolic space. These groups have a fundamental domain ℛ with the property that the geodesic planes containing each face are part of the tesselation. We use this map together with the methods of thermodynamic formalism to give another proof that the Selberg zeta function for such groups has a meromorphic extension to ℂ.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 119 , Issue 1 , January 1996 , pp. 179 - 190
Copyright
Copyright © Cambridge Philosophical Society 1996

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