Ramanujan-type congruences modulo m for (l, m)-regular bipartitions

Abstract

Let \(B_{l,m}(n)\) denote the number of (l, m)-regular bipartitions of n. Recently, many authors proved several infinite families of congruences modulo 3, 5 and 11 for \(B_{l,m}(n)\). In this paper, we use theta function identities to prove infinite families of congruences modulo m for (l, m)-regular bipartitions, where \(m\in \{7,3,11,13,17\}\).