Particular values of the Riemann zeta function

The Riemann zeta function, denoted as \(\zeta(s)\), is a complex function defined for complex numbers \(s\) with \(\text{Re}(s) > 1\) through the series: \[ \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s} \] It can also be analytically continued to other values of \(s\) (with the exception of \(s