Resurgence, Habiro elements and strange identities
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
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| _version_ | 1866918088381825024 |
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| author | Crew, Samuel Fantini, Veronica Goswami, Ankush Osburn, Robert Wheeler, Campbell |
| author_facet | Crew, Samuel Fantini, Veronica Goswami, Ankush Osburn, Robert Wheeler, Campbell |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07001 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Resurgence, Habiro elements and strange identities Crew, Samuel Fantini, Veronica Goswami, Ankush Osburn, Robert Wheeler, Campbell Number Theory Mathematical Physics Geometric Topology 57K16, 11F37, 30B40, 40A05 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. |
| title | Resurgence, Habiro elements and strange identities |
| topic | Number Theory Mathematical Physics Geometric Topology 57K16, 11F37, 30B40, 40A05 |
| url | https://arxiv.org/abs/2304.07001 |