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) = ^∞_n=1a_n {s λ_n} with the abscissa of absolute convergence σ a = 0, conditions on (λ_n) and (a_n) (λn) are established under which M(σ, F) = T_R(1 + o(1)) {ρ R/|σ|} as σ 0, whereM(σ, F) = {|F(σ + it)| : t R} and T_R and ρ_R are positive constants.