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Tr. Inst. Mat., 2012, Volume 20, Number 2, Pages 51–63 (Mi timb173)  

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

On the frequency of integer polynomials with a given number of close roots

D. U. Kaliada

Institute of Mathematics of the National Academy of Sciences of Belarus

Abstract: In the paper is considered the relation between number of integer polynomials of some degree having a given number of close real roots on the upper bound for diameter of this root cluster. There was established the asymptotics of that relation as the root cluster diameter tends to zero and maximal height of polynomials tends to infinity. The lower bound for the number of integer polynomial of given degree with bounded height and bounded discriminant is obtained.

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UDC: 511.35, 511.48, 511.75
Received: 22.10.2012

Citation: D. U. Kaliada, “On the frequency of integer polynomials with a given number of close roots”, Tr. Inst. Mat., 20:2 (2012), 51–63

Citation in format AMSBIB
\Bibitem{Kol12}
\by D.~U.~Kaliada
\paper On the frequency of integer polynomials with a given number of close roots
\jour Tr. Inst. Mat.
\yr 2012
\vol 20
\issue 2
\pages 51--63
\mathnet{http://mi.mathnet.ru/timb173}


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    This publication is cited in the following articles:
    1. J. Math. Sci. (N. Y.), 229:6 (2018), 664–670  mathnet  crossref  mathscinet
  • Труды Института математики
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