Twisted dynamical zeta functions and the Fried's conjecture

TL;DR

This survey explores twisted dynamical zeta functions, their relation to Fried's conjecture, and discusses complex-valued analytic torsion within the context of Ruelle and Selberg zeta functions.

Contribution

It provides an overview of the current state of research on twisted dynamical zeta functions and Fried's conjecture, highlighting recent developments and open problems.

Findings

Summarizes key results on twisted Ruelle and Selberg zeta functions.

Discusses the connection between zeta functions and analytic torsion.

Identifies open questions in the field.

Abstract

This is a survey article on the twisted dynamical zeta functions of Ruelle and Selberg and the Fried's conjecture. It is based on the mini-course: "Twisted Ruelle zeta function, complex-valued analytic torsion and the Fried's conjecture", given by the author during the thematic trimester programme: "Representation Theory and Noncommutative Geometry" at the Institut Henri Poincar\'{e}.