Holomorphic torsion for Hermitian locally symmetric spaces

TL;DR

This paper explores the holomorphic torsion of compact Hermitian locally symmetric spaces, expressing it as a special value of a zeta function derived from geometric data like closed geodesics.

Contribution

It provides a new formula linking holomorphic torsion to zeta functions based on geometric features of Hermitian locally symmetric spaces.

Findings

Holomorphic torsion is expressed as a zeta function value.

The approach connects geometric data with spectral invariants.

Provides a framework for computing torsion using geometric information.

Abstract

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