A note on congruences for generalized cubic partitions modulo primes
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915176102494208 |
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| author | Guadalupe, Russelle |
| author_facet | Guadalupe, Russelle |
| contents | Recently, Amdeberhan, Sellers, and Singh introduced the notion of a generalized cubic partition function $a_c(n)$ and proved two isolated congruences via modular forms, namely, $a_3(7n+4)\equiv 0\pmod{7}$ and $a_5(11n+10)\equiv 0\pmod{11}$. In this paper, we provide another proof of these congruences by using classical $q$-series manipulations. We also give infinite families of congruences for $a_c(n)$ for primes $p\not\equiv 1\pmod{8}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_15628 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A note on congruences for generalized cubic partitions modulo primes Guadalupe, Russelle Number Theory Combinatorics 05A17, 11F03, 11P83 Recently, Amdeberhan, Sellers, and Singh introduced the notion of a generalized cubic partition function $a_c(n)$ and proved two isolated congruences via modular forms, namely, $a_3(7n+4)\equiv 0\pmod{7}$ and $a_5(11n+10)\equiv 0\pmod{11}$. In this paper, we provide another proof of these congruences by using classical $q$-series manipulations. We also give infinite families of congruences for $a_c(n)$ for primes $p\not\equiv 1\pmod{8}$. |
| title | A note on congruences for generalized cubic partitions modulo primes |
| topic | Number Theory Combinatorics 05A17, 11F03, 11P83 |
| url | https://arxiv.org/abs/2407.15628 |