Analytic Continuations of Riemann Zeta Function

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Theorem

Right half-plane

The Riemann zeta function has a unique analytic continuation to $\set {s \in \C : \map \Re s > 0} \setminus \set 1$, the half-plane $\map \Re s > 0$ minus the point $s = 1$.


Complex plane

The Riemann zeta function $\zeta$ has a unique analytic continuation to $\C\setminus\{1\}$.


Also see