# Definition:Half-Plane of Convergence

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 $f$.