Multipartite Generating Functions and Infinite Products for Quantum Invariants
Mathematical Physics
2017-02-09 v1 High Energy Physics - Theory
math.MP
Abstract
We show that multipartite generation functions can be written in terms of the Bell polynomials (known as Fa\`a 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.
Keywords
Cite
@article{arxiv.1702.02208,
title = {Multipartite Generating Functions and Infinite Products for Quantum Invariants},
author = {A. A. Bytsenko and M. Chaichian},
journal= {arXiv preprint arXiv:1702.02208},
year = {2017}
}
Comments
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