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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2502.17312 |
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| _version_ | 1866913705196781568 |
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| author | B., Hemanthkumar S, Sumanth Bharadwaj H. |
| author_facet | B., Hemanthkumar S, Sumanth Bharadwaj H. |
| contents | Recently, several mathematicians have investigated various partition functions with the goal of discovering Ramanujan-type congruences. One such function is $\overline{B}_{2^α}(n)$, which represents the number of $2^α-$regular overpartition pairs of $n$. In this context, we establish Ramanujan-type congruences modulo powers of $2$ for this function. For instance, we prove that \begin{equation*} \overline{B}_{2^α}(2^{α+β+1}(n+1)) \equiv 0\pmod{2^{3β+5}} \end{equation*} for all $n, β\geq 0,\, α\in \mathbb{N}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_17312 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Arithmetic properties of $2^α-$Regular overpartition pairs B., Hemanthkumar S, Sumanth Bharadwaj H. Number Theory 05A17, 11P83 (Primary) Recently, several mathematicians have investigated various partition functions with the goal of discovering Ramanujan-type congruences. One such function is $\overline{B}_{2^α}(n)$, which represents the number of $2^α-$regular overpartition pairs of $n$. In this context, we establish Ramanujan-type congruences modulo powers of $2$ for this function. For instance, we prove that \begin{equation*} \overline{B}_{2^α}(2^{α+β+1}(n+1)) \equiv 0\pmod{2^{3β+5}} \end{equation*} for all $n, β\geq 0,\, α\in \mathbb{N}$. |
| title | Arithmetic properties of $2^α-$Regular overpartition pairs |
| topic | Number Theory 05A17, 11P83 (Primary) |
| url | https://arxiv.org/abs/2502.17312 |