scholarly journals Divisor of the Selberg zeta function for kleinian groups

1994 ◽  
pp. 1-9
Author(s):  
Peter A. Perry
Keyword(s):  
Zeta Function ◽  
Kleinian Groups ◽  
Selberg 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.

scholarly journals Normal modes in thermal AdS via the Selberg zeta function

2020 ◽  
Vol 9 (1) ◽  
Author(s):  
Victoria Martin ◽  
Andrew Svesko
Keyword(s):  
Zeta Function ◽  
Heat Kernel ◽  
Normal Mode ◽  
Kernel Method ◽  
Normal Modes ◽  
Quasinormal Mode ◽  
Partition Functions ◽  
Selberg Zeta Function ◽  
Exact Agreement ◽  
Spin Fields

The heat kernel and quasinormal mode methods of computing 1-loop partition functions of spin ss fields on hyperbolic quotient spacetimes \mathbb{H}^{3}/\mathbb{Z}ℍ3/ℤ are related via the Selberg zeta function. We extend that analysis to thermal \text{AdS}_{2n+1}AdS2n+1 backgrounds, with quotient structure \mathbb{H}^{2n+1}/\mathbb{Z}ℍ2n+1/ℤ. Specifically, we demonstrate the zeros of the Selberg function encode the normal mode frequencies of spin fields upon removal of non-square-integrable modes. With this information we construct the 1-loop partition functions for symmetric transverse traceless tensors in terms of the Selberg zeta function and find exact agreement with the heat kernel method.

Sign in / Sign up

Export Citation Format

Share Document