English

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