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

作者：Xia, Ernest X. W.; Yao, Olivia X. M.^*

来源：Journal of Number Theory, 2017, 171: 1-17.

DOI：10.1016/j.jnt.2016.06.017

• Congruence
• Regular partition
• Bipartition
• Ramanujan's theta function

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

• 出版日期2017-2
• 单位江苏大学