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

2022/12/09 by Yiwen Lu, Xuejun Guo, Lu, Yiwen +1
Mathematics · #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2212.05013

openalex publication_date 2022/12/09 · openalex created_date 2022/12/25 · openalex updated_date 2026/07/28

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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