Restricted divisor functions and half Appell sums in higher-level
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915483910930432 |
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| author | Tian, Meng-Juan Zhou, Nian Hong |
| author_facet | Tian, Meng-Juan Zhou, Nian Hong |
| contents | We examine the value distributions of coefficients in certain $q$-series related to half Appell sums in higher-level and the first moment of the Garvan's $k$-rank of partitions. We prove that these coefficients equal certain restricted divisor functions and can take any nonnegative integer value infinitely many times. As applications, we confirm a conjecture of Xiong on the coefficients of a half Lerch sum and a conjecture of Garvan and Jennings-Shaffer on the nonnegativity of spt-crank-type partitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_06032 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Restricted divisor functions and half Appell sums in higher-level Tian, Meng-Juan Zhou, Nian Hong Number Theory Primary 11P82, Secondary 11N37 We examine the value distributions of coefficients in certain $q$-series related to half Appell sums in higher-level and the first moment of the Garvan's $k$-rank of partitions. We prove that these coefficients equal certain restricted divisor functions and can take any nonnegative integer value infinitely many times. As applications, we confirm a conjecture of Xiong on the coefficients of a half Lerch sum and a conjecture of Garvan and Jennings-Shaffer on the nonnegativity of spt-crank-type partitions. |
| title | Restricted divisor functions and half Appell sums in higher-level |
| topic | Number Theory Primary 11P82, Secondary 11N37 |
| url | https://arxiv.org/abs/2509.06032 |