Multiple zeta function

The multiple zeta function is a generalization of the classical Riemann zeta function, which plays a significant role in number theory and mathematical analysis. The classical Riemann zeta function is defined for complex numbers \( s \) with real part greater than 1 as: \[ \zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s}. \] The multiple zeta function extends this idea to multiple variables.