Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2017, Volume 142, Pages 42–56 (Mi into252)  
The order of the Dirichlet series in the half-strip

A. M. Gaisina, N. N. Aitkuzhinab

a Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
b Bashkir State University, Ufa
Full-text PDF (224 kB)
Abstract: We study Dirichlet series converging in a half-plane whose sequence of exponents can be extended to a certain “regular” sequence. We prove that the $k$-orders of Dirichlet series are the same in all half-strips whose widths are greater than a certain number called the special density of distribution of exponents.
Keywords: $R_ {k}$-density of the sequence, the Dirichlet series, $k$-order, half-strip, half-plane.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00720
15-01-01661
This work was partially supported by the Russian Foundation for Basic Research (projects №№ 14-01-00720, 15-01-01661).
English version:
Journal of Mathematical Sciences, 2019, Volume 241, Issue 6, Pages 686–700
DOI: https://doi.org/10.1007/s10958-019-04455-y
Bibliographic databases:
Document Type: Article
UDC: 517.53
MSC: 30D10
Language: Russian
Citation: A. M. Gaisin, N. N. Aitkuzhina, “The order of the Dirichlet series in the half-strip”, Complex analysis, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 142, VINITI, M., 2017, 42–56; Journal of Mathematical Sciences, 241:6 (2019), 686–700
Citation in format AMSBIB
\Bibitem{GaiAit17}
\by A.~M.~Gaisin, N.~N.~Aitkuzhina
\paper The order of the Dirichlet series in the half-strip
\inbook Complex analysis
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2017
\vol 142
\pages 42--56
\publ VINITI
\publaddr M.
\mathnet{http://mi.mathnet.ru/into252}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3801348}
\zmath{https://zbmath.org/?q=an:1426.30004}
\transl
\jour Journal of Mathematical Sciences
\yr 2019
\vol 241
\issue 6
\pages 686--700
\crossref{https://doi.org/10.1007/s10958-019-04455-y}
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