Analogues of Wiman's theorem for Dirichlet series

This paper studies the classes of integral functions $f$ that are given by a Dirichlet series which converges absolutely in the whole plane and has nonnegative indices and are such that $\ln M(x)\sim\ln\mu(x)$ as $x\to\infty$ outside some exceptional set, where $M(x)=\sup\{|f(x+iy)|:|y|<\infty\}$ and $\mu(x)$ is the maximum term in the Dirichlet series.
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