 Landau theorem for a Dirichlet series with nonnegative coefficients

If a Dirichlet series with nonnegative coefficients has finite abscissa of convergence ${\sigma }_c$, then the function it defines has a singularity at the real point $s={\sigma }_c$. Consequently, if that function extends holomorphically across every real point, the original series converges for every real $s$.