Abstract:
We study the Dirichlet series converging only in a half-plane such that their sequence of exponents admits an extension to a “regular” sequence. We proved the exactness of two-sided estimates for k-order of the sum of the Dirichlet series in a semi-strip whose width depends on the special distribution density of the exponents.
Keywords:k-order of the Dirichlet series in a semi-strip, entire functions with a prescribed asymptotics on the positive axis.
\Bibitem{AitGai15}
\by N.~N.~Aitkuzhina, A.~M.~Gaisin
\paper Exactness of estimates for $k$th order of Dirichlet series in a~semi-strip
\jour Ufa Math. J.
\yr 2015
\vol 7
\issue 4
\pages 15--23
\mathnet{http://mi.mathnet.ru/eng/ufa298}
\crossref{https://doi.org/10.13108/2015-7-4-15}
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Linking options:
https://www.mathnet.ru/eng/ufa298
https://doi.org/10.13108/2015-7-4-15
https://www.mathnet.ru/eng/ufa/v7/i4/p15
This publication is cited in the following 2 articles:
A. M. Gaisin, G. A. Gaisina, “Order of Dirichlet series with regular distribution of exponents in half-strips”, Ufa Math. J., 10:4 (2018), 50–63
A. M. Gaisin, N. N. Aitkuzhina, “The order of the Dirichlet series in the half-strip”, J. Math. Sci. (N. Y.), 241:6 (2019), 686–700
Citation in format AMSBIB
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