Arithmetic properties for ( s , t )-regular bipartition functions
Arithmetic properties for ( s , t )-regular bipartition functions
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DOI：
10.1016/j.jnt.2016.06.017
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发表时间：
2017-02
影响因子：
0.7
通讯作者：
Ernest X. W. Xia;Olivia X. M. Yao
中科院分区：
文献类型：
--
作者：
Ernest X. W. Xia;Olivia X. M. Yao
设B s，t（n）表示（s，t）-正则二分划的个数.最近，Dou发现了B 3，11（n）的模11同余的无穷族.她还提出了几个关于B s，t（n）的证明。本文利用Berndt书中出现的一个θ函数恒等式，证明了Dou关于B 3，7（n）的三个定理.此外，我们还证明了B 3，s（n）和B 5，s（n）的模3和模5同余的几个无限族.此外，利用纽曼的恒等式，我们证明了B 3，7（n）的模7同余的许多无穷族.
Let B s, t (n) denote the number of (s, t)-regular bipartitions. Recently, Dou discovered an infinite family of congruences modulo 11 for B 3, 11 (n). She also presented several conjectures on B s, t (n). In this paper, utilizing an theta function identity appeared in Berndt's book, we confirm three conjectures on B 3, 7 (n) given by Dou. Moreover, we prove several infinite families of congruences modulo 3 and 5 for B 3, s (n) and B 5, s (n). In addition, we prove many infinite families of congruences modulo 7 for B 3, 7 (n) by employing an identity of Newman.