Arithmetic properties for (s,t)-regular bipartition functions

Let Bs,t(n) denote the number of (s,t)-regular bipartitions. Recently, Dou discovered an infinite family of congruences modulo 11 for B3,11(n). She also presented several conjectures on Bs,t(n). In this paper, utilizing an theta function identity appeared in Berndt's book, we confirm three conjectures on B3,7(n) given by Dou. Moreover, we prove several infinite families of congruences modulo 3 and 5 for B3,s(n) and B5,s(n). In addition, we prove many infinite families of congruences modulo 7 for B3,7(n) by employing an identity of Newman.