Year: 2025
Type: article
Abstract: In this paper, we study the twisted Ruelle zeta function associated with the geodesic flow of a compact, hyperbolic, odd-dimensional manifold X. The twisted Ruelle zeta function is associated with an acyclic representation $\chi \colon \pi _{1}(X) \rightarrow \operatorname {\mathrm {GL}}_{n}(\mathbb {C})$ , which is close enough to an acyclic, unitary representation. In this case, the twisted Ruelle zeta function is regular at zero and equals the square of the refined analytic torsion, as it is introduced by Braverman and Kappeler in [6], multiplied by an exponential, which involves the eta invariant of the even part of the odd-signature operator, associated with $\chi $ .
Author: Polyxeni Spilioti
Institution: National Technical University of Athens
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
Award: G4749558751
OpenAlex ID: W4406648727