The divisor of Selberg's zeta function for Kleinian groups

2001 ◽  
Vol 106 (2) ◽  
pp. 321-390 ◽  
Author(s):  
S. J. Patterson ◽  
Peter A. Perry
Keyword(s):  
Zeta Function ◽  
Kleinian Groups ◽  
Selberg’S Zeta Function

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

1996 ◽  
Vol 119 (1) ◽  
pp. 179-190
Author(s):  
André Rocha
Keyword(s):  
Zeta Function ◽  
Hyperbolic Space ◽  
Fundamental Domain ◽  
Thermodynamic Formalism ◽  
Kleinian Groups ◽  
Selberg Zeta Function ◽  
3 Dimensional ◽  
Expanding Map

AbstractWe 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.

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