Holomorphic torsion and closed geodesics

TL;DR

This paper explores the relationship between holomorphic torsion in hermitian locally symmetric spaces and special values of geometric zeta functions, providing new insights into their mathematical structure.

Contribution

It introduces a novel expression of holomorphic torsion as a special value of a geometric zeta function, linking geometric analysis and number theory.

Findings

Holomorphic torsion can be represented via geometric zeta functions.

Establishes a new connection between torsion invariants and zeta function values.

Provides a framework for further study of spectral invariants in symmetric spaces.

Abstract

The holomorphic torsion of a hermitian locally symmetric space is expressed as a special value of a geometric zeta function.