On the growth of an entire dirichlet series - Sheremeta, M. M. (Ukrains’kyi Matematychnyi Zhurnal, 1999)
We establish the relation between the increase of the quantityM(σ,F) = ∣a 0∣ + ∑ n=1 ∞ ∣a n ∣ exp (σλ n ) and the behavior of sequences (|a n |) and (λ n ), where (λ n ) is a sequence of nonnegative numbers increasing to + ∞, andF(s) =a 0 + ∑ n=1 ∞ a n e sλn ,s=σ+it, is the Dirichlet entire series.