# Definition:Half-Plane of Convergence

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## Definition

Let $f \left({s}\right)$ be a (general) Dirichlet series.

The half-plane of convergence of $f$ is the set:

$\left\{ {s: s \in \C, \operatorname{Re} \left({s}\right) > \sigma_0}\right\}$

where $\sigma_0$ is abscissa of convergence of $f$.