Analytic torsion of finite volume hyperbolic orbifolds

TL;DR

This paper defines the analytic torsion for finite volume hyperbolic orbifolds and investigates its asymptotic behavior along specific representation paths.

Contribution

It introduces a new definition of analytic torsion for finite volume orbifolds and analyzes its asymptotic properties in this setting.

Findings

Established the definition of analytic torsion for finite volume hyperbolic orbifolds.

Derived asymptotic behavior of the torsion along certain representation rays.

Provides insights into spectral invariants of orbifolds with finite volume.

Abstract

In this article we define the analytic torsion of finite volume orbifolds $\Gamma \backslash \mathbb{H}^{2n+1}$ and study its asymptotic behavior with respect to certain rays of representations.