abscissa of convergence

《Algebraic Number Theory》 · 第 11 页 · Section 1.2「Analytic properties of Dirichlet series」，Corollary 1.2

Any Dirichlet series $\alpha(s)=\sum_{n=1}^{\infty}a_nn^{-s}$ has an abscissa of convergence $\sigma_c$ with the property that $\alpha(s)$ converges for all $s$ with $\sigma>\sigma_c$, and for no $s$ with $\sigma<\sigma_c$.