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.
References
A. F. Leont’ev,Series of Exponents [in Russian], Nauka, Moscow (1976).
Additional information
Lviv University, Lviv. Translated from Ukrainskii Matematicheskii Zhurmal, Vol. 51, No. 8, pp. 1149–1153, August, 1999.
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Sheremeta, M.M. On the growth of an entire dirichlet series. Ukr Math J 51, 1296–1302 (1999). https://doi.org/10.1007/BF02592520
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DOI: https://doi.org/10.1007/BF02592520