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

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

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

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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• http://mi.mathnet.ru/eng/timb/v20/i2/p51

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This publication is cited in the following articles:
1. J. Math. Sci. (N. Y.), 229:6 (2018), 664–670
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