Arithmetic properties for a partition function related to the Ramanujan/Watson mock theta function $$\omega (q)$$ω(q)
Arithmetic properties for a partition function related to the Ramanujan/Watson mock theta function $$\omega (q)$$ω(q)
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DOI：
10.1007/s11139-018-0004-0
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发表时间：
2018-05
期刊：
影响因子：
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通讯作者：
Ernest X. W. Xia
中科院分区：
文献类型：
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作者：
Ernest X. W. Xia
最近，Andrews，Dianjin和Yee引入了一个新的分区函数，表示nin中每个奇数部分小于最小部分的两倍的分区数。的生成函数与三阶模拟θ函数相关联。安德鲁斯，帕萨里，塞勒斯，和余证明了三个无限家庭的同余模4和8的，并提供了初等证明的同余模5的首次发现的瓦尔德赫尔。本文证明了模5和模2的幂的一些新的同余式。特别地，我们得到了一些非标准同余。例如，我们证明了，和。
Recently, Andrews, Dixit, and Yee introduced a new partition functionthat denotes the number of partitions ofnin which each odd part is less than twice the smallest part. The generating function ofis associated with the third-order mock theta function. Andrews, Passary, Sellers, and Yee proved three infinite families of congruences modulo 4 and 8 forand provided elementary proofs of congruences modulo 5 forwhich were first discovered by Waldherr. In this paper, we prove some new congruences modulo 5 and powers of 2 for. In particular, we obtain some non-standard congruences for. For example, we prove that for,and.