Let M(σ) = sup{|F(σ + it)|: t ∈ ℝ} and µ(σ) = max {|a n |exp(σλn): n ≥ 0}, σ < 0, for a Dirichlet series {fx995-01} with abscissa of absolute convergence σa = 0. We prove that the condition ln ln n = o(ln λn), n → ∞, is necessary and sufficient for the equivalence of the relations {fx995-02}, for each series of this type.
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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 6, pp. 851–856, June, 2008.
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Mulyava, O.M., Sheremeta, M.M. On conditions for Dirichlet series absolutely convergent in a half-plane to belong to the class of convergence. Ukr Math J 60, 995–1002 (2008). https://doi.org/10.1007/s11253-008-0097-5
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DOI: https://doi.org/10.1007/s11253-008-0097-5