Reciprocals of false theta functions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911087648047104 |
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| author | Keith, William J. |
| author_facet | Keith, William J. |
| contents | We investigate reciprocals of false theta functions, producing results such as congruences, simple asymptotic bounds, and combinatorial identities. Of particular interest is a connection between $1/Ψ(-q^2,q)$ and the truncated pentagonal number theorem of Andrews and Merca. We record a useful dissection identity analogous to the known theta function dissection. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_19998 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Reciprocals of false theta functions Keith, William J. Combinatorics 05A17, 11F27 We investigate reciprocals of false theta functions, producing results such as congruences, simple asymptotic bounds, and combinatorial identities. Of particular interest is a connection between $1/Ψ(-q^2,q)$ and the truncated pentagonal number theorem of Andrews and Merca. We record a useful dissection identity analogous to the known theta function dissection. |
| title | Reciprocals of false theta functions |
| topic | Combinatorics 05A17, 11F27 |
| url | https://arxiv.org/abs/2412.19998 |