Short proof of Rademacher's formula for partitions

2018/01/18 by Wladimir de Azevedo Pribitkin, Brandon Williams, Pribitkin, Wladimir de Azevedo +1 · 1 citation
Mathematics · #11F20 #11P82 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1801.06244

openalex publication_date 2018/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

Abstract

This note rederives a formula for r-color partitions, 1 ≤ r ≤ 24, including Rademacher's celebrated result for ordinary partitions, from the duality between modular forms of weights -r/2 and 2+r/2.

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• Rademacher-type exact formula and higher order Turán inequalities for r-colored ℓ-regular partitions

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