The Riemann zeta function is defined as the analytic continuation of the function defined for σ > 1 by the sum of the preceding series.

The Riemann zeta function, $ζ(s)$, is a function of a complex variable $s$ that analytically continues the sum of the infinite series

$$\zeta(s) =\sum_{n=1}^\infty\frac{1}{n^s}$$

which converges when the real part of $s$ is greater than $1$.

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