Analytic torsions associated with the Rumin complex on contact spheres

TL;DR

This paper computes the eigenvalues of the Rumin Laplacian on contact spheres and expresses the associated analytic torsion functions using the Riemann zeta function, revealing their properties and values.

Contribution

It explicitly determines all eigenvalues of the Rumin Laplacian on contact spheres and expresses the analytic torsion functions in terms of the Riemann zeta function, providing new explicit formulas.

Findings

Eigenvalues of the Rumin Laplacian are explicitly computed.

Analytic torsion functions are expressed in terms of the Riemann zeta function.

The torsion functions vanish at the origin and their values are determined.

Abstract

We explicitly write down all eigenvalues of the Rumin Laplacian on the standard contact spheres, and express the analytic torsion functions associated with the {Rumin complex} in terms of the Riemann zeta function. In particular, we find that the functions vanish at the origin and determine the analytic torsions.