scholarly journals Dynamical zeta functions, Nielsen theory and Reidemeister torsion

2000 ◽  
Vol 147 (699) ◽  
pp. 0-0 ◽  
Author(s):  
Alexander Fel′shtyn
Keyword(s):  
Zeta Functions ◽  
Reidemeister Torsion ◽  
Nielsen Theory

scholarly journals Ruelle Zeta Functions of Hyperbolic Manifolds and Reidemeister Torsion

2021 ◽  
Author(s):  
Werner Müller
Keyword(s):  
Fundamental Group ◽  
General Result ◽  
Hyperbolic Manifold ◽  
Zeta Functions ◽  
Hyperbolic Manifolds ◽  
Reidemeister Torsion ◽  
Finite Dimensional ◽  
Orthogonal Representations ◽  
Ruelle Zeta Function ◽  
Complex Valued

AbstractThis paper is concerned with the behavior of twisted Ruelle zeta functions of compact hyperbolic manifolds at the origin. Fried proved that for an orthogonal acyclic representation of the fundamental group of a compact hyperbolic manifold, the twisted Ruelle zeta function is holomorphic at $$s=0$$ s = 0 and its value at $$s=0$$ s = 0 equals the Reidemeister torsion. He also established a more general result for orthogonal representations, which are not acyclic. The purpose of the present paper is to extend Fried’s result to arbitrary finite dimensional representations of the fundamental group. The Reidemeister torsion is replaced by the complex-valued combinatorial torsion introduced by Cappell and Miller.

Zeta functions in Nielsen theory

1988 ◽  
Vol 22 (1) ◽  
pp. 76-78 ◽  
Author(s):  
A. L. Fel'shtyn
Keyword(s):  
Zeta Functions ◽  
Nielsen Theory
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