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

  • B. V. Vynnyts’kyi

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 $(−∞,+∞)$.
Published
25.12.1997
How to Cite
Vynnyts’kyiB. V. “On the Growth of Functions Represented by Dirichlet Series With Complex Coefficients on the Real Axis”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 49, no. 12, Dec. 1997, pp. 1610–1616. December, https://umj.imath.kiev.ua/index.php/umj/article/view/5165.
Section
Research articles