Mathematical Proceedings of the Cambridge Philosophical Society: Volume 119 -

Meromorphic extension of the Selberg zeta function for Kleinian groups via thermodynamic formalism
André Rocha
Published online by Cambridge University Press:

24 October 2008, pp. 179-190
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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.

Mathematical Proceedings of the Cambridge Philosophical Society