Transformation formula Dedekind´s eta function

Transformation formula Dedekind´s eta function

December 27, 2022

In this blog entry we prove the transformation formula for the Dedekind´s eta function

$\eta(\tau)=e^{\pi i \tau / 12} \prod_{n=1}^\infty \left(1-e^{2 \pi i n \tau} \right)$

$\begin{align*} \eta\left( -\frac{1}{\tau}\right)&=\sqrt{-i \tau}\,\,\eta\left( \tau\right) \end{align*}$

The proof is due to C.L. Siegel, and it´s done by contour integration.

Click here to read it.

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