Arithmetic Properties modulo powers of $2$ and $3$ for Overpartition $k$-Tuples with Odd Parts
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| Format: | Preprint |
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2024
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| _version_ | 1866917440962691072 |
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| author | Das, Hirakjyoti Saikia, Manjil P. Sarma, Abhishek |
| author_facet | Das, Hirakjyoti Saikia, Manjil P. Sarma, Abhishek |
| contents | Recently, Drema and N. Saikia (2023) and M. P. Saikia, Sarma, and Sellers (2023) proved several congruences modulo powers of $2$ for overpartition triples with odd parts. In this paper, we study further divisibility properties of overpartition $k$-tuples with odd parts using elementary means as well as properties of modular forms. In particular, we prove several congruences modulo multiples of $3$, and an infinite family of congruences modulo powers of $3$; we also prove some cases of a conjecture of Saikia, Sarma, and Sellers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_02929 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Arithmetic Properties modulo powers of $2$ and $3$ for Overpartition $k$-Tuples with Odd Parts Das, Hirakjyoti Saikia, Manjil P. Sarma, Abhishek Number Theory 11P81, 11P83 Recently, Drema and N. Saikia (2023) and M. P. Saikia, Sarma, and Sellers (2023) proved several congruences modulo powers of $2$ for overpartition triples with odd parts. In this paper, we study further divisibility properties of overpartition $k$-tuples with odd parts using elementary means as well as properties of modular forms. In particular, we prove several congruences modulo multiples of $3$, and an infinite family of congruences modulo powers of $3$; we also prove some cases of a conjecture of Saikia, Sarma, and Sellers. |
| title | Arithmetic Properties modulo powers of $2$ and $3$ for Overpartition $k$-Tuples with Odd Parts |
| topic | Number Theory 11P81, 11P83 |
| url | https://arxiv.org/abs/2409.02929 |