New Ramanujan-type congruences for overpartitions modulo $11$ and $13$
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866915846777995264 |
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| author | Wei, XuanLing |
| author_facet | Wei, XuanLing |
| contents | In this paper, we establish two new Ramanujan-type congruences for the overpartition function: $\overline{p}(11\times(8n+5))\equiv 0 \pmod{11}$ and $\overline{p}(13\times 2^6(8n+7))\equiv 0 \pmod{13}$. The proofs rely on the theory of modular forms. We conjecture potential Ramanujan-type congruences for overpartitions modulo 7, 17, 19 and 23. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08510 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | New Ramanujan-type congruences for overpartitions modulo $11$ and $13$ Wei, XuanLing Number Theory 11P83 In this paper, we establish two new Ramanujan-type congruences for the overpartition function: $\overline{p}(11\times(8n+5))\equiv 0 \pmod{11}$ and $\overline{p}(13\times 2^6(8n+7))\equiv 0 \pmod{13}$. The proofs rely on the theory of modular forms. We conjecture potential Ramanujan-type congruences for overpartitions modulo 7, 17, 19 and 23. |
| title | New Ramanujan-type congruences for overpartitions modulo $11$ and $13$ |
| topic | Number Theory 11P83 |
| url | https://arxiv.org/abs/2603.08510 |