On the Calculus of the Spectrum of the Laplacian for functions in Lens Spaces

TL;DR

This paper refines a method to determine the eigenspace dimensions of the Laplace-Beltrami operator on lens spaces, providing explicit results for eigenvalues and eigenspace parity, advancing spectral geometry understanding.

Contribution

It introduces an improved technique for calculating eigenspace dimensions on lens spaces, with applications to eigenvalue explicit descriptions and eigenspace parity analysis.

Findings

Explicit formulas for eigenspace dimensions

Determination of smallest positive eigenvalue

Parity results for eigenspaces

Abstract

We improve a specific method to obtain the dimension of the eigenspaces of the Laplace-Beltrami operator on lens spaces and establish some applications related to the explicit description of the dimension of the smallest positive eigenvalue and the parity of the dimensions of the eigenspaces.