On conditions for Dirichlet series absolutely convergent in a half-plane to belong to the class of convergence - Mulyava, O. M.; Sheremeta, M. M. (Ukrains’kyi Matematychnyi Zhurnal, 2008)
For a Dirichlet series F(s) = ^∞_n=0a_n {sλ_n} with the abscissa of absolute convergence σ_a = 0, let M(σ) = {|F(σ+it)|: t R} and μ(σ) = {|a_n| (σ λ_n): n ≥ 0},σ < 0. It is proved that the condition n = o(λ_n), n→∞, is necessary and sufficient for equivalence of relations ^0_-1|σ|^ρ-1M(σ)dσ < +∞ and ^0_-1|σ|^ρ-1μ(σ)dσ < +∞,ρ > 0, for each such series.