Riemann zeta function

Definition

The Riemann zeta function, denoted $\zeta$ (pronounced zeta), is a holomorphic function defined on $\mathbb{C}\setminus \{1\}$.

Definition in terms of the summation representation

For $s$ such that $\mathrm{R}\mathrm{e}(s)>1$, we have:

$\zeta (s)=\sum _{n=1}^{\mathrm{\infty }}\frac{1}{n^s}$