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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2023, Number 1, Pages 25–35
DOI: https://doi.org/10.26907/0021-3446-2023-1-25-35 (Mi ivm9845) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the stability of the maximum term of the Dirichlet series

A. M. Gaisina, G. A. Gaisinab

a Institute of Mathematics with Computing Centre Ufa Federal Research Centre of Russian Academy of Science, 112 Chernyshevsky str., Ufa, 450008 Russia
b Bashkir State University, 32 Zaki Validy str., Ufa, 450076 Russia
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DOI: https://doi.org/10.26907/0021-3446-2023-1-25-35
Abstract: We study the behavior of the maximum term of the modified Dirichlet series with positive exponents, the sum of which is an entire function. In this article, we prove a criterion for the equivalence of the logarithm of the maximum term of the original series and of the logarithm of the maximum term of the the modified series on the asymptotic set for the class of entire Dirichlet series defined by some convex majorant of growth. The corresponding problem on the stability of the maximum term for entire Dirichlet series of arbitrary growth was studied by the first author in connection with the Polya problem on the asymptotic behavior of entire transcendental functions on curves going to infinity.
Keywords: Dirichlet series, maximal term, convex majorant, Hadamard composition, Young transform.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation 075-02-2022-1826
Received: 15.03.2022
Revised: 18.05.2022
Accepted: 29.06.2022
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2023, Volume 67, Issue 1, Pages 20–29
DOI: https://doi.org/10.3103/S1066369X23010024
Document Type: Article
UDC: 517.53
Language: Russian
Citation: A. M. Gaisin, G. A. Gaisina, “On the stability of the maximum term of the Dirichlet series”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 1, 25–35; Russian Math. (Iz. VUZ), 67:1 (2023), 20–29
Citation in format AMSBIB
\Bibitem{GaiGai23}
\by A.~M.~Gaisin, G.~A.~Gaisina
\paper On the stability of the maximum term of the Dirichlet series
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2023
\issue 1
\pages 25--35
\mathnet{http://mi.mathnet.ru/ivm9845}
\crossref{https://doi.org/10.26907/0021-3446-2023-1-25-35}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2023
\vol 67
\issue 1
\pages 20--29
\crossref{https://doi.org/10.3103/S1066369X23010024}
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    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
     
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