Dedekind eta function (awaiting review)

We define the Dedekind eta function $\eta(z)$ by the formula \[ \eta(z)=q^{1/24}\prod_{n\geq1}(1-q^n), \] where $q=e^{2\pi iz}$.

The Dedekind eta function is a crucial example of a half-integral weight modular form, having weight $1/2$ and level $1$.

It is related to the Discriminant modular form via the formula \[ \Delta(z)=\eta^{24}(z). \]