Divisibility and distribution of 5-regular partitions

Qi-Yang Zheng

Divisibility and distribution of 5-regular partitions

Number Theory 2022-08-04 v1

Authors: Qi-Yang Zheng

Abstract

In this paper we study $b_5(n)$ , the $5$ -regular partitions of $n$ . Using the theory of modular forms, we prove several theorems on the divisibility and distribution properties of $b_5(n)$ modulo prime $m\geq5$ . In particular, we prove that there are infinitely many Ramanujan-type congruences modulo prime $m\geq5$ .

Keywords

regular partitions divisibility distribution modular forms ramanujan congruences

Cite

@article{arxiv.2206.03696,
  title  = {Divisibility and distribution of 5-regular partitions},
  author = {Qi-Yang Zheng},
  journal= {arXiv preprint arXiv:2206.03696},
  year   = {2022}
}

Comments

7 pages. arXiv admin note: text overlap with arXiv:2205.03191

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