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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2204.02628 |
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| _version_ | 1866911960980783104 |
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| author | Goswami, Ankush Jha, Abhash Kumar Kim, Byungchan Osburn, Robert |
| author_facet | Goswami, Ankush Jha, Abhash Kumar Kim, Byungchan Osburn, Robert |
| contents | We prove asymptotics and study sign patterns for coefficients in expansions of elements in the Habiro ring which satisfy a strange identity. As an application, we prove asymptotics and discuss positivity for the generalized Fishburn numbers which arise from the Kontsevich-Zagier series associated to the colored Jones polynomial for a family of torus knots. This extends Zagier's result on asymptotics for the Fishburn numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2204_02628 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Asymptotics and sign patterns for coefficients in expansions of Habiro elements Goswami, Ankush Jha, Abhash Kumar Kim, Byungchan Osburn, Robert Number Theory Combinatorics 05A16, 13B35, 57K16, 11B83 We prove asymptotics and study sign patterns for coefficients in expansions of elements in the Habiro ring which satisfy a strange identity. As an application, we prove asymptotics and discuss positivity for the generalized Fishburn numbers which arise from the Kontsevich-Zagier series associated to the colored Jones polynomial for a family of torus knots. This extends Zagier's result on asymptotics for the Fishburn numbers. |
| title | Asymptotics and sign patterns for coefficients in expansions of Habiro elements |
| topic | Number Theory Combinatorics 05A16, 13B35, 57K16, 11B83 |
| url | https://arxiv.org/abs/2204.02628 |