Multipartite Generating Functions and Infinite Products for Quantum Invariants
arXiv:1702.02208
Abstract
We show that multipartite generation functions can be written in terms of the Bell polynomials (known as Faà di Bruno's formula) and the Ruelle spectral functions, whose spectrum is encoded in the Patterson-Selberg function of the hyperbolic three-geometry. We derive an infinite-product formula for the Chern-Simons partition functions and analyze appropriate q-series which leads to the construction of knot invariants. With the help of the Ruelle spectral functions symmetric and modular properties in infinite-product structure can be described.
Dedicated to the memory of our friend and colleague, Petya Kulish. arXiv admin note: substantial text overlap with arXiv:1602.06704; text overlap with arXiv:1012.2636 by other authors