Modular discriminant ($\Delta$)

The modular discriminant is the normalized weight-twelve level-one cusp form

For every real $s$, the rapidly convergent integralis the analytic continuation of $(2\pi {)}^{-s}\Gamma (s)L(\Delta ,s)$. The product for $\Delta$ makes the integrand positive, so $L(\Delta ,s)>0$ for real $s>0$.