Analogues of Ramanujan’s partition identities
Analogues of Ramanujan’s partition identities
复制标题
DOI：
10.1007/s11139-012-9439-x
复制
发表时间：
2013-08
期刊：
影响因子：
--
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
Ramanujan发现其中p（n）是n的划分数。最近，H. C. Chan和S.库珀和H. Chan和P.C. Toh建立了几个类似的拉马努金的分区身份采用理论的模块功能。最近，N。Baruah和K.K. Ojah研究了定义为$$\sum_{n=0}^\infty p_{[c^ld^m]}（n）q^n= \frac{1}{\prod_{j=1}^\infty（1-q^{cj}）^{l}（1-q^{dj}）^m}的配分函数。$$他们发现了一些类似的拉马努金的分区身份，并推导出几个有趣的分区同余。在本文中，我们提供了一个统一的方法来证明他们的一些结果，利用加法公式。在这个过程中，我们还建立了一些新的Ramanujan的分拆恒等式和同余式。
Ramanujan discovered thatwherep(n) is the number of partitions ofn. Recently, H.-C. Chan and S. Cooper, and H.H. Chan and P.C. Toh established several analogues of Ramanujan’s partition identities by employing the theory of modular functions. Very recently, N.D. Baruah and K.K. Ojah studied the partition functionwhich is defined by $$\sum_{n=0}^\infty p_{[c^ld^m]}(n)q^n= \frac{1}{\prod_{j=1}^\infty (1-q^{cj})^{l}(1-q^{dj})^m}. $$ They discovered some analogues of Ramanujan’s partition identities and deduced several interesting partition congruences. In this paper, we provide a uniform method to prove some of their results by utilizing an addition formula. In the process, we also establish some new analogues of Ramanujan’s partition identities and congruences for.