Rademacher's Formula for the Partition Function

2023/02/08 by Kong, Ze-Yong, Teo, Lee-Peng
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2302.03835

Abstract

For a positive integer n, let p(n) be the number of ways to express n as a sum of positive integers. In this note, we revisit the derivation of the Rademacher's convergent series for p(n) in a pedagogical way, with all the details given. We also derive the leading asymptotic behavior of p(n) when n approaches infinity. Some numerical results are tabled.

Related

• Simple alternative to the Hardy-Ramanujan-Rademacher formula for p(N)
• An expansion for the number of partitions of an integer
• Error bounds for the asymptotic expansion of the partition function
• Disproof of a conjecture by Rademacher on partial fractions
• A Rademacher-type exact formula for partitions without sequences