Arithmetic Properties of Generalized Cubic and Overcubic Partitions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866910170775289856 |
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| author | Das, Hirakjyoti Maity, Saikat Saikia, Manjil P. |
| author_facet | Das, Hirakjyoti Maity, Saikat Saikia, Manjil P. |
| contents | We prove several congruences satisfied by the generalized cubic and generalized overcubic partition functions, recently introduced by Amdeberhan, Sellers, and Singh. We also prove infinite families of congruences modulo powers of $2$ and modulo $12$ satisfied by the generalized overcubic partitions, as well as some density results that they satisfy. We use both elementary $q$-series techniques as well as the theory of modular forms to prove our results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_19399 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Arithmetic Properties of Generalized Cubic and Overcubic Partitions Das, Hirakjyoti Maity, Saikat Saikia, Manjil P. Number Theory 05A17, 11F03, 11P83 We prove several congruences satisfied by the generalized cubic and generalized overcubic partition functions, recently introduced by Amdeberhan, Sellers, and Singh. We also prove infinite families of congruences modulo powers of $2$ and modulo $12$ satisfied by the generalized overcubic partitions, as well as some density results that they satisfy. We use both elementary $q$-series techniques as well as the theory of modular forms to prove our results. |
| title | Arithmetic Properties of Generalized Cubic and Overcubic Partitions |
| topic | Number Theory 05A17, 11F03, 11P83 |
| url | https://arxiv.org/abs/2503.19399 |