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Zap. Nauchn. Sem. POMI, 2016, Volume 449, Pages 60–68 (Mi znsl6322)  

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

Critical values and moduli of derivative of a complex polynomial at its zeros

V. N. Dubininab

a Far Eastern Federal University, Vladivostok, Russia
b Institute for Applied Mathematics, Far Eastern Branch, Russian Academy of Sciences, Vladivostok, Russia

Abstract: Under some restrictions on critical values of an algebraic polynomial with complex coefficients, a sharp inequality for the product of certain powers of moduli of its derivatives at its zeros is established. The equality is attained for the suitable Chebyshev polynomial of the first kind.

Key words and phrases: polynomial, Chebyshov polynomial, critial values, symmetrization.

Funding Agency Grant Number
Russian Science Foundation 14-11-00022


Full text: PDF file (187 kB)
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English version:
Journal of Mathematical Sciences (New York), 2017, 225:6, 877–882

Bibliographic databases:

Document Type: Article
UDC: 517.54
Received: 10.07.2016

Citation: V. N. Dubinin, “Critical values and moduli of derivative of a complex polynomial at its zeros”, Analytical theory of numbers and theory of functions. Part 32, Zap. Nauchn. Sem. POMI, 449, POMI, St. Petersburg, 2016, 60–68; J. Math. Sci. (N. Y.), 225:6 (2017), 877–882

Citation in format AMSBIB
\Bibitem{Dub16}
\by V.~N.~Dubinin
\paper Critical values and moduli of derivative of a~complex polynomial at its zeros
\inbook Analytical theory of numbers and theory of functions. Part~32
\serial Zap. Nauchn. Sem. POMI
\yr 2016
\vol 449
\pages 60--68
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl6322}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3580131}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2017
\vol 225
\issue 6
\pages 877--882
\crossref{https://doi.org/10.1007/s10958-017-3503-4}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85027297825}


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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. V. N. Dubinin, “Poyas lemniskat i teoremy iskazheniya dlya mnogolistnykh funktsii”, Analiticheskaya teoriya chisel i teoriya funktsii. 33, Posvyaschaetsya pamyati Galiny Vasilevny KUZMINOI, Zap. nauchn. sem. POMI, 458, POMI, SPb., 2017, 17–30  mathnet
  • Записки научных семинаров ПОМИ
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