On the regular growth of Dirichlet series absolutely convergent in a half-plane - Stets', Yu. V.; Sheremeta, M. M. (Ukrains’kyi Matematychnyi Zhurnal, 2011)
For the Dirichlet series $F(s) = \sum^{∞}_{n=1}a_n \exp \{s λ_n\}$ with the abscissa of absolute convergence $σ a = 0$, conditions on $(λ_n)$ and $(a_n)$ (λn) are established under which $\ln M(σ, F) = T_R(1 + o(1)) \exp\{ρ R/|σ|\}$ as$σ \uparrow 0$, where$M(σ, F) = \sup\{|F(σ + it)| : t \in R\}$ and $T_R$ and $ρ_R$ are positive constants.