English

Analytic torsion, dynamical zeta function, and the Fried conjecture for admissible twists

Differential Geometry 2021-06-02 v1 Dynamical Systems

Abstract

We show an equality between the analytic torsion and the absolute value at the zero point of the Ruelle dynamical zeta function on a closed odd dimensional locally symmetric space twisted by an acyclic flat vector bundle obtained by the restriction of a representation of the underlying Lie group. This generalises author's previous result for unitarily flat vector bundles, and the results of Br\"ocker, M\"uller, and Wotzke on closed hyperbolic manifolds.

Keywords

Cite

@article{arxiv.2009.04897,
  title  = {Analytic torsion, dynamical zeta function, and the Fried conjecture for admissible twists},
  author = {Shu Shen},
  journal= {arXiv preprint arXiv:2009.04897},
  year   = {2021}
}

Comments

40 pages. arXiv admin note: text overlap with arXiv:2009.03427

R2 v1 2026-06-23T18:26:46.920Z