Landau theorem for a Dirichlet series with nonnegative coefficients
= Landau theorem for a Dirichlet series with nonnegative coefficients
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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 $s$.