Elliptic genera and characteristic q-series of superconformal field theory

We analyze the characteristic series, the KO series and the series associated with the Witten genus, and their analytic forms as the q-analogs of classical special functions (in particular q-analog of the beta integral and the gamma function). q-Series admit an analytic interpretation in terms of the spectral Ruelle functions, and their relations with appropriate elliptic modular forms can be described. We show that there is a deep correspondence between the characteristic series of the Witten genus and KO   characteristic series, on one side, and the denominator identities and characters of N=2N=2 superconformal algebras, and the affine Lie (super)algebras on the other. We represent the characteristic series in the form of double series using the Hecke–Rogers modular identity.