On the partial fraction decomposition of the restricted partition generating function

2014/01/13 by Cormac O'Sullivan, Cormac O’Sullivan, O'Sullivan, Cormac
Mathematics · #11B68 #11P82 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11B68 #msc:11P82

paper · pdf · doi:10.48550/arxiv.1401.2809

arxiv created 2014/01/13 · openalex publication_date 2014/01/13 · arxiv updated 2014/01/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide new formulas for the coefficients in the partial fraction decomposition of the restricted partition generating function. These techniques allow us to partially resolve a recent conjecture of Sills and Zeilberger. We also describe upcoming work, giving a resolution to Rademacher's conjecture on the asymptotics of these coefficients.

Related

• Asymptotics for the partial fractions of the restricted partition generating function I
• Disproof of a conjecture by Rademacher on partial fractions
• Asymptotics for the partial fractions of the restricted partition generating function II
• Simple proofs and expressions for the restricted partition function and its polynomial part
• Rademacher's conjecture and expansions at roots of unity of products\n generating restricted partitions