Restricted Overpartitions and concave compositions: their modularity and asymptotics
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908934079512576 |
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| author | Banerjee, Koustav Bringmann, Kathrin Dixit, Atul |
| author_facet | Banerjee, Koustav Bringmann, Kathrin Dixit, Atul |
| contents | In this paper we study restricted overpartitions and concave compositions. In several cases the resulting generating functions involve simultaneously modular forms, mock theta functions, mock Maass theta functions, and false theta functions, illustrating the appearance of mixed modular structures in restricted partition problems. Moreover, we obtain their asymptotic main terms. We also study related rank statistics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_03998 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Restricted Overpartitions and concave compositions: their modularity and asymptotics Banerjee, Koustav Bringmann, Kathrin Dixit, Atul Number Theory Combinatorics 11F03, 11F37, 11P82, 11P83, 33D15 In this paper we study restricted overpartitions and concave compositions. In several cases the resulting generating functions involve simultaneously modular forms, mock theta functions, mock Maass theta functions, and false theta functions, illustrating the appearance of mixed modular structures in restricted partition problems. Moreover, we obtain their asymptotic main terms. We also study related rank statistics. |
| title | Restricted Overpartitions and concave compositions: their modularity and asymptotics |
| topic | Number Theory Combinatorics 11F03, 11F37, 11P82, 11P83, 33D15 |
| url | https://arxiv.org/abs/2601.03998 |