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) = \frac{1}{1^z} + \frac{1}{2^z} + \frac{1}{3^z} + \frac{1}{4^z} + \cdots \right) \end{equation}