Determinant of Friederichs Dirichlet Laplacians on $2$-dimensional hyperbolic cones

TL;DR

This paper derives an explicit formula for the spectral determinant of Friedrichs Dirichlet Laplacians on 2D hyperbolic cones, correcting previous inaccuracies in related research.

Contribution

It provides a new explicit expression for the spectral determinant on hyperbolic cones, addressing errors in recent related literature.

Findings

Explicit formula for spectral determinant in terms of cone angle and boundary radius

Identification and correction of errors in recent related results

Enhanced understanding of spectral properties on hyperbolic cones

Abstract

We explicitly express the spectral determinant of Friederichs Dirichlet Laplacians on the 2-dimensional hyperbolic (Gaussian curvature -1) cones in terms of the cone angle and the geodesic radius of the boundary. The related results in the recent paper "Riemann-Roch isometries in the non-compact orbifold setting," J. Eur. Math. Soc. 22 (2020) by G. Freixas i Montplet and A. von Pippich turn out to be incorrect.