Riemann zeta function

$\zeta (s)={\sum }_{n\ge 1}{n}^{-s}$ for $\Re s>1$; its Euler product is ${\prod }_p(1-p^{-s}{)}^{-1}$.

The Riemann zeta function, denoted as \(\zeta(s)\), is a complex function defined for complex numbers \(s = \sigma + it\), where \(\sigma\) and \(t\) are real numbers.