A D4881: Complex function $\zeta : \mathbb{C} \to \mathbb{C}$ is a Riemann zeta function if and only if

(1)	$\zeta$ is an D1411: Analytic complex function
(2)	\begin{equation} \forall \, z \in \mathbb{C} \left( \Re(z) > 1 \quad \implies \quad \zeta(z) = \sum_{n = 1}^{\infty} \frac{1}{n^z} \right) \end{equation}