Dynamical zeta functions for geodesic flows and the higher-dimensional Reidemeister torsion for Fuchsian groups
-
Yoshikazu Yamaguchi
Abstract
We show that the absolute value at zero of
the Ruelle zeta function defined by the geodesic flow
coincides with the higher-dimensional Reidemeister torsion
for the unit tangent bundle over a 2-dimensional hyperbolic orbifold
and a non-unitary representation of the fundamental group.
Our proof is based on the integral expression of the Ruelle zeta function.
This integral expression is derived from the functional equation of the Selberg zeta function for
a discrete subgroup with elliptic elements in
Funding source: Japan Society for the Promotion of Science
Award Identifier / Grant number: 17K05240
Funding statement: The work was supported by JSPS KAKENHI Grant Number 17K05240.
Acknowledgements
The author would like to express his thanks to the referee for his/her careful reading and helpful comments to improve the manuscript.
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Monodromy of elliptic curve convolution, seven-point sheaves of G2 type, and motives of Beauville type
- Long time behavior of discrete volume preserving mean curvature flows
- Morse quasiflats I
- Numerical equivalence of ℝ-divisors and Shioda–Tate formula for arithmetic varieties
- Dynamical zeta functions for geodesic flows and the higher-dimensional Reidemeister torsion for Fuchsian groups
- The inertial Jacquet–Langlands correspondence
- Total mean curvature of the boundary and nonnegative scalar curvature fill-ins
- The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups
Artikel in diesem Heft
- Frontmatter
- Monodromy of elliptic curve convolution, seven-point sheaves of G2 type, and motives of Beauville type
- Long time behavior of discrete volume preserving mean curvature flows
- Morse quasiflats I
- Numerical equivalence of ℝ-divisors and Shioda–Tate formula for arithmetic varieties
- Dynamical zeta functions for geodesic flows and the higher-dimensional Reidemeister torsion for Fuchsian groups
- The inertial Jacquet–Langlands correspondence
- Total mean curvature of the boundary and nonnegative scalar curvature fill-ins
- The strong geometric lemma for intrinsic Lipschitz graphs in Heisenberg groups
