Ramanujan-Type Congruences for $(\ell ,m)$-Regular Bipartitions Modulo 2, 5 and 7

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2024年11月9日

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Murugan Palani,
Syeda Noor Fathima

摘要

In this article, by employing some theta identities of Ramanujan, we establish many Ramanujan-type congruences modulo 2, 5 and 7 for $B_{\ell ,m}(n)$ $B_{ℓ, m} (n)$ , where $(\ell ,m)\in \{(2,21), (5,14), (5,21), (5,28), (5,49), (5,343), (6,16), (14,28), (22,44)\}$ $(ℓ, m) \in {(2, 21), (5, 14), (5, 21), (5, 28), (5, 49), (5, 343), (6, 16), (14, 28), (22, 44)}$ .

Ramanujan-Type Congruences for \((\ell ,m)\)-Regular Bipartitions Modulo 2, 5 and 7

摘要