Divisibility and distribution of 5-regular partitions

2022/06/08 by Qi-Yang Zheng, Zheng, Qi-Yang
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2206.03696

openalex publication_date 2022/06/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study b₅(n), the 5-regular partitions of n. Using the theory of modular forms, we prove several theorems on the divisibility and distribution properties of b₅(n) modulo prime m≥5. In particular, we prove that there are infinitely many Ramanujan-type congruences modulo prime m≥5.

Related

• Distribution of 3-regular and 5-regular partitions
• Distribution of the partition function modulo m
• New congruences for 4,6-regular partitions modulo primes
• Infinite Families of Congruences Modulo 5 for Ramanujan's General Partition Function
• Arithmetic properties of 5-regular partitions into distinct parts