2019
Том 71
№ 9

All Issues

On the growth of an entire dirichlet series

Sheremeta M. M.

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Abstract

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.

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