\begin{definition}[Definition:Riemann Zeta Function]
The '''Riemann Zeta Function''' $\zeta$ is the complex function defined on the half-plane $\map \Re s > 1$ as the series:
:$\ds \map \zeta s = \sum_{n \mathop = 1}^\infty \frac 1 {n^s}$
\end{definition}