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arXiv · 2212.05013

Distribution of the k-regular partition function modulo composite integers M

Yiwen Lu·Xuejun Guo
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Abstract

Let $b_k(n)$ denote the $k-$regular partitons of a natural number $n$. In this paper, we study the behavior of $b_k(n)$ modulo composite integers $M$ which are coprime to $6$. Specially, we prove that for arbitrary $k-$regular partiton function $b_k(n)$ and integer $M$ coprime to $6$, there are infinitely many Ramanujan-type congruences of $b_k(n)$ modulo $M$.

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Yiwen Lu, Xuejun Guo. 2022-12-09. Distribution of the k-regular partition function modulo composite integers M. https://arxiv.org/abs/2212.05013

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