On conditions for Dirichlet series absolutely convergent in a half-plane to belong to the class of convergence |
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Authors: | O M Mulyava M M Sheremeta |
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Institution: | (1) Kyiv National University of Food Technology, Kyiv, Ukraine;(2) Lviv National University, Lviv, Ukraine |
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Abstract: | 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.
Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 6, pp. 851–856, June, 2008. |
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