Recall the Riemann-Zeta function is given by \begin{align*} \zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s} = \prod_{p\text{ prime}} {1 \over 1 - p^{-s}} .\end{align*}

which is the Euler product expansion of the classical Riemann-Zeta function.

Recall that the Riemann-Zeta function has a product expansion