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

Yiwen Lu; Xuejun Guo

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

Number Theory 2022-12-12 v1

Authors: Yiwen Lu , Xuejun Guo

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 $M$ .

Keywords

partition congruences partition theory ramanujan identities and series

Cite

@article{arxiv.2212.05013,
  title  = {Distribution of the k-regular partition function modulo composite integers M},
  author = {Yiwen Lu and Xuejun Guo},
  journal= {arXiv preprint arXiv:2212.05013},
  year   = {2022}
}

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