Equivariant torsion of locally symmetric spaces

TL;DR

This paper expresses the equivariant holomorphic torsion of compact locally symmetric spaces as a special value of a zeta function derived from geometric data like closed geodesics.

Contribution

It provides a new formula linking equivariant torsion to zeta functions based on geometric features of the space.

Findings

Equivariant torsion is expressed as a zeta function value.

The formula involves geometric data such as closed geodesics.

This links spectral invariants to geometric and dynamical data.

Abstract

The equivariant holomorphic torsion of a compact locally symmetric manifold and an automorphism is expressed as a special value of a zeta function built out of geometric data (closed geodesics) of the manifold.