Turkish Journal of Mathematics
DOI
10.3906/mat-1512-62
Abstract
In this paper, we investigate the arithmetic properties of $\ell$-regular overpartition pairs. Let $\overline{B}_{\ell}(n)$ denote the number of $\ell$-regular overpartition pairs of $n$. We will prove the number of Ramanujan-like congruences and infinite families of congruences modulo 3, 8, 16, 36, 48, 96 for $\overline{B}_3(n)$ and modulo 3, 16, 64, 96 for $\overline{B}_4(n)$. For example, we find that for all nonnegative integers $\alpha$ and $n$, $\overline{B}_{3}(3^{\alpha}(3n+2))\equiv 0\pmod{3}$, $\overline{B}_{3}(3^{\alpha}(6n+4))\equiv 0\pmod{3}$, and $\overline{B}_{4}(8n+7)\equiv 0\pmod{64}$.
Keywords
Congruences, theta function, overpartition pair, regular partition
First Page
756
Last Page
774
Recommended Citation
NAIKA, MEGADAHALLI SIDDANAIKA MAHADEVA and SHIVASHANKAR, CHANDRAPPA
(2017)
"Arithmetic properties of $\ell$-regular overpartition pairs,"
Turkish Journal of Mathematics: Vol. 41:
No.
3, Article 25.
https://doi.org/10.3906/mat-1512-62
Available at:
https://journals.tubitak.gov.tr/math/vol41/iss3/25