Dedekind eta function

In mathematics, the Dedekind eta function, named after Richard Dedekind, is a modular form of weight 1/2 and is a function defined on the upper half-plane of complex numbers, where the imaginary part is positive.

For any complex number τ with Im(τ) > 0, let q = exp(2π i τ), and define the eta function by,

The notation ${\displaystyle q\equiv e^{2\pi {\rm {{i}\tau }}}\,}$ is now standard in number theory, though many older books use q for the nome ${\displaystyle e^{\pi {\rm {{i}\tau }}}\,}$. Raising the eta equation to the 24th power and multiplying by (2π)¹² gives

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