Ze-Yong Kong

collaborators

2 papers

math.NT2023

Rademacher's Formula for the Partition Function

Ze-Yong Kong, Lee-Peng Teo

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 se…

math.NT2023

An Elementary Proof of the Transformation Formula for the Dedekind Eta Function

Ze-Yong Kong, Lee-Peng Teo

The Dedekind eta function $η (τ)$ is defined by \[η(τ)=e^{πiτ/12}\prod_{n=1}^{\infty}\left(1-e^{2πi nτ}\right),\quad\text{when}\;\text{Im}\,τ>0.\] It plays an important role in numb…