Resurgence, Habiro elements and strange identities
Number Theory
2025-07-14 v3 Mathematical Physics
Geometric Topology
math.MP
Abstract
We prove resurgence properties for the Borel transform of a formal power series associated to elements in the Habiro ring that come from radial limits of partial theta series via strange identities. As an application, we prove a conjecture in quantum topology due to Costin and Garoufalidis for two families of torus knots.
Keywords
Cite
@article{arxiv.2304.07001,
title = {Resurgence, Habiro elements and strange identities},
author = {Samuel Crew and Veronica Fantini and Ankush Goswami and Robert Osburn and Campbell Wheeler},
journal= {arXiv preprint arXiv:2304.07001},
year = {2025}
}
Comments
20 pages, to appear in Communications in Number Theory and Physics