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

Ze-Yong Kong, Lee-Peng Teo

The Dedekind eta function $\eta (\tau )$ 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…