Parity of the partition function in quadratic progressions

2025/09/11 by Ono, Ken
#05A17 #11G20 #11P82 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2509.09553

Abstract

The parity of the partition function p(n) remains strikingly mysterious. Beyond a handful of fragmentary results, essentially nothing is known about the distribution of parity. We prove a uniform result on quadratic progressions. If 1

Citations

• The partition function and elliptic curves
• The partition function modulo 4
• Algebraic formulas for the coefficients of half-integral weight harmonic weak Maass forms
• Automorphic forms onO s +2,2(R) and infinite products

Related

• A combinatorial proof on partition function parity
• Combinatorial proof of an inequality on some partitions separated by parity
• On the asymptotic behavior for partitions separated by parity
• Partitions in real quadratic fields
• Parity of the Partition Function p(n,k)