Dedekind eta function

Summary

The Dedekind eta function is $\eta(\tau) = e^{\pi i \tau / 12} \prod_{n \ge 1} (1 - e^{2 \pi i n \tau})$ on the upper half-plane. It is holomorphic and never zero there, and it transforms like a modular form of weight $1/2$, up to $24$-th roots of unity. Its $24$-th power is the cusp form $\Delta$ of weight $12$. Its reciprocal is, up to a factor, the generating function of the partition function.