On the growth of functions represented by Dirichlet series with complex coefficients on the real axis - Vynnyts’kyi, B. V. (Ukrains’kyi Matematychnyi Zhurnal, 1997)
We establish conditions under which, for a Dirichlet series F(z) = _n = 1^∞ d n (λ_n z), the inequality ⋎F(x)⋎ ≤ y(x),x ≥ x_0, implies the relation _n = 1^∞ |d_n (λ_n z)| ⪯ γ((1 + o(1))x) as x → +∞, where γ is a nondecreasing function on (−∞,+∞).