The asymptotics of the Ray-Singer analytic torsion for compact hyperbolic manifolds

TL;DR

This paper investigates the asymptotic behavior of Ray-Singer analytic torsion in compact hyperbolic manifolds, focusing on specific representation rays derived from the isometry group, enhancing understanding of geometric spectral invariants.

Contribution

It provides new asymptotic formulas for analytic torsion associated with particular representation rays in hyperbolic manifolds, extending previous spectral analysis results.

Findings

Asymptotic formulas for analytic torsion derived

Behavior characterized for specific representation rays

Enhanced understanding of spectral invariants in hyperbolic geometry

Abstract

In this paper we study the asymptotic behavior of the analytic torsion for compact, oriented hyperbolic manifolds with respect to certain rays of representations obtained by restriction of irreducible representations of the group of isometries of the hyperbolic space