Abstract
We establish conditions under which, for a Dirichlet series F(z) = Σ ∞ n = 1 d n exp(λ n z), the inequality ⋎F(x)⋎≤y(x),x≥x o, implies the relation Σ ∞ n = 1 |d n exp(λ n z)| ⪯ γ((1 + o(1))x) as x→+∞, where γ is a nondecreasing function on (−∞,+∞).
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Additional information
Franko Drohobych State Pedagogic Institute, Drohobych. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 12, pp. 1610–1616. December, 1997
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Vynnyts’kyi, B.V., Shapovalovs’kyi, O.V. On the growth of functions represented by Dirichlet series with complex coefficients on the real axis. Ukr Math J 49, 1810–1818 (1997). https://doi.org/10.1007/BF02513060
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DOI: https://doi.org/10.1007/BF02513060