The partition function modulo 4

2022/12/13 by Ken Ono, Ono, Ken · 2 citations
Mathematics · #05A17 #11P83 #Advanced Algebra and Geometry #Advanced Mathematical Identities #Analytic Number Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2212.06935

openalex publication_date 2022/12/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is widely believed that the parity of the partition function p(n) is ``random.'' Contrary to this expectation, in this note we prove the existence of infinitely many congruence relations modulo 4 among its values. For each square-free integer 1

Cited by

• Parity of the partition function in quadratic progressions
• The partition function and elliptic curves

Related

• Explicit linear dependence congruence relations for the partition function modulo 4
• Distribution of the partition function modulo m
• Parity of the Partition Function p(n,k)
• Modulo 2 congruences for partitions with initial repetitions
• Scarcity of congruences for the partition function