2017
Том 69
№ 7

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On the growth of functions represented by Dirichlet series with complex coefficients on the real axis

Vynnyts’kyi B. V.

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Abstract

We establish conditions under which, for a Dirichlet series $F(z) = \sum_{n = 1}^{∞} d n \exp(λ_n z)$, the inequality $⋎F(x)⋎ ≤ y(x),\quad x ≥ x_0$, implies the relation $\sum_{n = 1}^{∞} |d_n \exp(λ_n z)| ⪯ γ((1 + o(1))x)$ as $x → +∞$, where $γ$ is a nondecreasing function on $(−∞,+∞)$.

English version (Springer): Ukrainian Mathematical Journal 49 (1997), no. 12, pp 1810-1818.

Citation Example: Vynnyts’kyi B. V. On the growth of functions represented by Dirichlet series with complex coefficients on the real axis // Ukr. Mat. Zh. - 1997. - 49, № 12. - pp. 1610–1616. December.

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