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arXiv · 1603.09101

Some Congruences of a Restricted Bipartition Function

Nipen Saikia·Chayanika Boruah
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Abstract

Let $c_N(n)$ denotes the number of bipartitions $(\lambda, \mu)$ of a positive integer $n$ subject to the restriction that each part of $\mu$ is divisible by $N$. In this paper, we prove some congruence properties of the function $c_N(n)$ for $N=7$, 11, and $5l$, for any integer $l\ge 1$, by employing Ramanujan's theta-function identities.

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Nipen Saikia, Chayanika Boruah. 2016-03-30. Some Congruences of a Restricted Bipartition Function. https://arxiv.org/abs/1603.09101

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