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Mat. Zametki, 1998, Volume 63, Issue 3, Pages 457–467 (Mi mz1303)  

This article is cited in 1 scientific paper (total in 1 paper)

Sequences of maximal terms and central exponents of derivatives of Dirichlet series

M. N. Sheremeta

Ivan Franko National University of L'viv

Abstract: For the Dirichlet series corresponding to a function $F$ with positive exponents increasing to $\infty$ and with abscissa of absolute convergence $A\in(-\infty,+\infty]$, it is proved that the sequences $(\mu(\sigma,F^{(m)}))$ of maximal terms and $(\Lambda(\sigma,F^{(m)}))$ of central exponents are nondecreasing to $\infty$ as $m\to\infty$ for any given $\sigma<A$, and
$$ \varlimsup_{m\to\infty}\frac{\ln\mu(\sigma,F^{(m)})}{m\ln m}\le1 \quadand\quad \varlimsup_{m\to\infty}\frac{\ln\Lambda(\sigma,F^{(m)})}{\ln m}\le1. $$
Necessary and sufficient conditions for putting the equality sign and replacing $\varlimsup$ by $\lim$ in these relations are given.

DOI: https://doi.org/10.4213/mzm1303

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English version:
Mathematical Notes, 1998, 63:3, 401–410

Bibliographic databases:

UDC: 517.537.2
Received: 01.04.1996

Citation: M. N. Sheremeta, “Sequences of maximal terms and central exponents of derivatives of Dirichlet series”, Mat. Zametki, 63:3 (1998), 457–467; Math. Notes, 63:3 (1998), 401–410

Citation in format AMSBIB
\Bibitem{She98}
\by M.~N.~Sheremeta
\paper Sequences of maximal terms and central exponents of derivatives of Dirichlet series
\jour Mat. Zametki
\yr 1998
\vol 63
\issue 3
\pages 457--467
\mathnet{http://mi.mathnet.ru/mz1303}
\crossref{https://doi.org/10.4213/mzm1303}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1631905}
\zmath{https://zbmath.org/?q=an:0915.30003}
\transl
\jour Math. Notes
\yr 1998
\vol 63
\issue 3
\pages 401--410
\crossref{https://doi.org/10.1007/BF02317789}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000075783100018}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Ya. V. Mikityuk, M. N. Sheremeta, O. M. Sumyk, “On the Young Conjugate Functions and the Behavior of the Maximal Terms of the Derivatives of Dirichlet Series”, Math. Notes, 69:1 (2001), 65–71  mathnet  crossref  crossref  mathscinet  zmath  isi
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