Symmetric Functions and q-Products with an Application to Theoretical Physics

Abstract

The main purpose of this paper is to show that the Poincaré q-polynomials admit a representation in terms of the symmetric functions and the Patterson-Selberg (or Ruelle-type) spectral functions. We have shown that the q-series elliptic genera can be expressed in terms of q-analogs of the classical special functions, specially the equivalence between the spectral Patterson-Selberg and the Ruelle functions. The main result of this manuscript is to show that this representation can be used in theoretical physics and we analyze them in terms of the Patterson-Selberg spectral function R (s).