Resurgence, Habiro elements and strange identities

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.

Authors

Veronica Fantini (ORCID: https://orcid.org/0009-0001-5829-2339)
Samuel Crew (ORCID: https://orcid.org/0000-0003-0508-7523)
Ankush Goswami (ORCID: https://orcid.org/0000-0002-2340-3852)
Campbell Wheeler
Robert Osburn (ORCID: https://orcid.org/0000-0001-8775-8321)

Institutions

University College Dublin (IE)
Okinawa Institute of Science and Technology Graduate University (JP)
Université Paris-Saclay (FR)
The University of Texas Rio Grande Valley (US)
Imperial College London (GB)
Institut des Hautes Études Scientifiques (FR)

Publication Details

Journal: Communications in Number Theory and Physics
Published: 2025-01-01
DOI: https://doi.org/10.4310/cntp.250531025857
Citations: 2
Primary Topic: Language, Linguistics, Cultural Analysis
Type: article
Field-Weighted Citation Impact: 20.85

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article

Resurgence, Habiro elements and strange identities

Veronica Fantini, Samuel Crew, Ankush Goswami, Campbell Wheeler et al.

Jan 1, 2025

2 citations

Communications in Number Theory and Physics

Language, Linguistics, Cultural Analysis

20.85

article

Resurgence, Habiro elements and strange identities

Veronica Fantini, Samuel Crew, Ankush Goswami, Campbell Wheeler, Robert Osburn

January 1, 2025article en

2 citations

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.

Communications in Number Theory and PhysicsVol. 19(2)

University College Dublin (IE), Okinawa Institute of Science and Technology Graduate University (JP), Université Paris-Saclay (FR), The University of Texas Rio Grande Valley (US), Imperial College London (GB), Institut des Hautes Études Scientifiques (FR)

Openalex Percentile: Top 1%

Language, Linguistics, Cultural Analysis

20.85

DOI Source OpenAlex

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Resurgence, Habiro elements and strange identities — Veronica Fantini, Samuel Crew, et al. · Communications in Number Theory and Physics (2025) | TGRS Research Map | TGRS