Abstract:
Let, F(z)=∞∑n=1aneλnz be an entire function represented in the whole of the plane by an absolutely convergent Dirichlet series such that
0⩽λ1<λ2<⋯,¯limn→∞lnnλn=μ∈[0,+∞).
The connection between the growth of the quantity
M(F;x)=sup
End the behaviour of |a_n| and \lambda_n as n\to \infty is described in general form.
\Bibitem{OskKal96}
\by V.~A.~Oskolkov, L.~I.~Kalinichenko
\paper Growth of entire functions represented by Dirichlet series
\jour Sb. Math.
\yr 1996
\vol 187
\issue 10
\pages 1545--1560
\mathnet{http://mi.mathnet.ru/eng/sm168}
\crossref{https://doi.org/10.1070/SM1996v187n10ABEH000168}
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Linking options:
https://www.mathnet.ru/eng/sm168
https://doi.org/10.1070/SM1996v187n10ABEH000168
https://www.mathnet.ru/eng/sm/v187/i10/p129
This publication is cited in the following 1 articles:
P. V. Filevich, “On influence of the arguments of coefficients of a power series expansion of an entire function on the growth of the maximum of its modulus”, Siberian Math. J., 44:3 (2003), 529–538