Determinant of Laplacian on a non-compact 3-dimensional hyperbolic manifold with finite volume

TL;DR

This paper computes the functional determinant of Laplace-type operators on a 3D non-compact hyperbolic manifold with finite volume using quadratures and the Selberg trace formula.

Contribution

It provides a novel explicit computation method for the determinant on such manifolds, linking spectral theory with geometric analysis.

Findings

Explicit formula for the determinant obtained

Connection established between spectral data and geometric structure

Method applicable to other non-compact hyperbolic manifolds

Abstract

The functional determinant of Laplace-type operators on the 3-dimensional non-compact hyperbolic manifold with invariant fundamental domain of finite volume is computed by quadratures and making use of the related terms of the Selberg trace formula.