Limiting behaviour and modular completions of MacMahon-like q-series
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909252018241536 |
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| author | Bringmann, Kathrin Craig, William van Ittersum, Jan-Willem Pandey, Badri Vishal |
| author_facet | Bringmann, Kathrin Craig, William van Ittersum, Jan-Willem Pandey, Badri Vishal |
| contents | Recently, MacMahon's generalized sum-of-divisor functions were shown to link partitions, quasimodular forms, and q-multiple zeta values. In this paper, we explore many further properties and extensions of these. Firstly, we address a question of Ono by producing infinite families of MacMahon-like functions that approximate the colored partition functions (and indeed other eta quotients). We further explore the MacMahon-like functions and discover new and suggestive arithmetic structure and modular completions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_08340 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Limiting behaviour and modular completions of MacMahon-like q-series Bringmann, Kathrin Craig, William van Ittersum, Jan-Willem Pandey, Badri Vishal Number Theory Combinatorics 11F03, 11A25, 11F50, 11F11 Recently, MacMahon's generalized sum-of-divisor functions were shown to link partitions, quasimodular forms, and q-multiple zeta values. In this paper, we explore many further properties and extensions of these. Firstly, we address a question of Ono by producing infinite families of MacMahon-like functions that approximate the colored partition functions (and indeed other eta quotients). We further explore the MacMahon-like functions and discover new and suggestive arithmetic structure and modular completions. |
| title | Limiting behaviour and modular completions of MacMahon-like q-series |
| topic | Number Theory Combinatorics 11F03, 11A25, 11F50, 11F11 |
| url | https://arxiv.org/abs/2402.08340 |