On the growth of an entire dirichlet series
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.
English version (Springer): Ukrainian Mathematical Journal 51 (1999), no. 8, pp 1296-1302.
Citation Example: Sheremeta M. M. On the growth of an entire dirichlet series // Ukr. Mat. Zh. - 1999. - 51, № 8. - pp. 1149–1153.