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Dal'nevost. Mat. Zh., 2015, Volume 15, Number 1, Pages 21–37 (Mi dvmg295)  

Effective estimations of the measure of the sets of real numbers in which integer polynomials take small value

N. V. Budarinaa, V. I. Bernikb, F. Götzec

a Institute for Applied Mathematics, Khabarovsk Division, Far-Eastern Branch of the Russian Academy of Sciences
b Institute of Mathematics of the National Academy of Sciences of Belarus
c Bielefeld University, Department of Mathematics

Abstract: In this paper we obtain the effective estimates in the terms of $n$ and $Q$ for the measure of the sets of real numbers with the given approximation property by algebraic numbers of degree $n$ and height bounded by $Q\in\mathbb{N}$.

Key words: integer polynomials, Lebesgue measure, approximation by algebraic numbers.

Full text: PDF file (165 kB)
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UDC: 511.42
MSC: Primary 11J83; Secondary 11K60, 11J68
Received: 23.02.2015

Citation: N. V. Budarina, V. I. Bernik, F. Götze, “Effective estimations of the measure of the sets of real numbers in which integer polynomials take small value”, Dal'nevost. Mat. Zh., 15:1 (2015), 21–37

Citation in format AMSBIB
\Bibitem{BudBerGot15}
\by N.~V.~Budarina, V.~I.~Bernik, F.~G\"otze
\paper Effective estimations of the measure of the sets of real numbers in which integer polynomials take small value
\jour Dal'nevost. Mat. Zh.
\yr 2015
\vol 15
\issue 1
\pages 21--37
\mathnet{http://mi.mathnet.ru/dvmg295}
\elib{http://elibrary.ru/item.asp?id=23527887}


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