Short proof of Rademacher's formula for partitions

TL;DR

This paper presents a concise derivation of Rademacher's formula for partition functions using the duality of modular forms, covering cases from r-color partitions to ordinary partitions.

Contribution

It offers a short proof of Rademacher's formula by leveraging the duality between specific modular forms, simplifying previous derivations.

Findings

Derived Rademacher's formula for r-color partitions

Unified proof for ordinary and r-color partitions

Highlights duality between modular forms of different weights

Abstract

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