Ramanujan tau function
= Ramanujan tau function
{c}
{title2=$\tau(n)$}
{wiki}
The Ramanujan tau function gives the <Fourier coefficients> at positive indices of the <modular discriminant>: $\Delta(z)=\sum_{n\geq1}\tau(n)q^n$, with $\tau(1)=1$. The <Serre derivative> and <vanishing of weight-fourteen level-one cusp forms> give $q\,d\Delta/dq=E_2\Delta$ and hence the convolution recurrence
$$
(1-n)\tau(n)=24\sum_{r=1}^{n-1}\sigma_1(r)\tau(n-r).
$$