# On length-holonomy spectrum of three dimensional compact hyperbolic manifolds

## TL;DR

This paper proves a strong uniqueness property for the length-holonomy spectrum of three-dimensional compact hyperbolic manifolds, utilizing the analytic features of associated zeta functions.

## Contribution

It establishes a strong multiplicity one type theorem for the length-holonomy spectrum in 3D hyperbolic manifolds, a novel result in spectral geometry.

## Key findings

- Proves a strong multiplicity one property for the spectrum.
- Uses analytic properties of Selberg-Gangolli-Wakayama zeta functions.
- Advances understanding of spectral uniqueness in hyperbolic geometry.

## Abstract

In this paper we establish a strong multiplicity one type property for the length-holonomy spectrum for the three dimensional compact hyperbolic spaces. We use the analytic properties of Selberg-Gangolli-Wakayama zeta functions associated to compact hyperbolic spaces.