Trace of heat kernel, spectral zeta function and isospectral problem for sub-laplacians

Abstract

In this article, we first study the trace for the heat kernel for the sub-Laplacian operator on the unit sphere in ℂn+1. Then we survey some results on the spectral zeta function which is induced by the trace of the heat kernel. In the second part of the paper, we discuss an isospectral problem in the CR setting.