Infinite families of arithmetic identities and congruences for bipartitions with 3-cores

Abstract

Let A3(n) denote the number of bipartitions of n that are 3-cores. By employing Ramanujan's simple theta function identities, we prove that A3(2n+1)=13 σ(6n+5), where σ(n) denotes the sum of the positive divisors of n. We also find several infinite families of arithmetic identities and congruences for A3(n), which include generalizations of some recent results on A3(n) by B.L.S. Lin (2014) [6].