Modular $q$-holonomic modules
Geometric Topology
2022-04-01 v1 High Energy Physics - Theory
Classical Analysis and ODEs
Abstract
We introduce the notion of modular -holonomic modules whose fundamental matrices define a cocycle with improved analyticity properties and show that the generalised -hypergeometric equation, as well as three key -holonomic modules of complex Chern--Simons theory are modular. This notion explains conceptually recent structural properties of quantum invariants of knots and 3-manifolds, and of exact and perturbative Chern--Simons theory, and in addition provides an effective method to solve the corresponding linear -difference equations. An alternative title of our paper, emphasising the equations rather than the modules, is: Modular linear -difference equations.
Cite
@article{arxiv.2203.17029,
title = {Modular $q$-holonomic modules},
author = {Stavros Garoufalidis and Campbell Wheeler},
journal= {arXiv preprint arXiv:2203.17029},
year = {2022}
}
Comments
65 pages, 5 figures