= Abscissa of absolute convergence of a Dirichlet series
{title2=$\sigma_a=\inf\{\sigma:\sum_n|a_n|n^{-\sigma}<\infty\}$}
<absolute convergence> of a <Dirichlet series> depends only on the <real part> of its variable. The set of real parts giving convergence is upward closed by the <comparison test>. If that set is nonempty and not all of the real line, its finite <infimum> is the abscissa: every larger real part gives convergence, and every smaller real part gives divergence. Boundary convergence is a separate question.
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