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 $f$.
Sources
- Dirichlet series. A.F. Leont'ev (originator),Encyclopedia of Mathematics. URL: https://www.encyclopediaofmath.org/index.php?title=Dirichlet_series