(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) = \lim_{N \to \infty} \sum_{n = 1}^N \frac{1}{n^z} \right) \end{equation} |
(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) = \lim_{N \to \infty} \sum_{n = 1}^N \frac{1}{n^z} \right) \end{equation} |
(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} |
(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} |
▶ | C2: Riemann hypothesis |