Parity of the coefficients of certain eta-quotients, III: two special classes
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| author | Keith, William J. Zanello, Fabrizio |
| author_facet | Keith, William J. Zanello, Fabrizio |
| contents | We continue a series of papers studying the parity of families of eta-quotients, which provide implications for the parity of the partition function as well as an overarching conjecture on related $q$-series. The present article focuses on two classes. One consists of eta-quotients of the form $f_t^3/f_1$, a distinguished case of Andrews' singular overpartitions that has recently attracted attention among researchers. In addition, we investigate the parity of certain pure eta-powers $f_1^t$, appending new results to known density theorems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_15716 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Parity of the coefficients of certain eta-quotients, III: two special classes Keith, William J. Zanello, Fabrizio Combinatorics Commutative Algebra Number Theory Primary: 11P83. Secondary: 05A17, 11P84, 11P82, 11F33 We continue a series of papers studying the parity of families of eta-quotients, which provide implications for the parity of the partition function as well as an overarching conjecture on related $q$-series. The present article focuses on two classes. One consists of eta-quotients of the form $f_t^3/f_1$, a distinguished case of Andrews' singular overpartitions that has recently attracted attention among researchers. In addition, we investigate the parity of certain pure eta-powers $f_1^t$, appending new results to known density theorems. |
| title | Parity of the coefficients of certain eta-quotients, III: two special classes |
| topic | Combinatorics Commutative Algebra Number Theory Primary: 11P83. Secondary: 05A17, 11P84, 11P82, 11F33 |
| url | https://arxiv.org/abs/2404.15716 |