Explicit computations of some spectral invariants of compact symmetric spaces of rank one

In this paper, we propose a unified approach for the study of the heat functions of the compact symmetric spaces of rank one. One of the consequences of this study is to show that the spectral properties of any compact symmetric space of rank one can be determined by a given polynomial. We prove that the coefficients of these polynomials are related to the Stirling numbers of the first kind. Moreover, we show that these polynomials possess some combinatorial interpretations, generalizing some combinatorial properties of Bernoulli numbers.