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Trudy Instituta Matematiki, 2018, Volume 26, Number 1, Pages 25–30 (Mi timb286)  

Complex algebraic numbers in the sets of $\mathbb{C}^2$ of small Lebesgue measure

V. I. Bernik, M. A. Zhur

Institute of Mathematics of the National Academy of Sciences of Belarus, Minsk
References:
Abstract: Algebraic numbers of degree $n$ are investigated. For any $Q \ge {Q_0}\left( n \right)$ we show lower bound for distribution of complex algebraic numbers of height less then $Q$ near a smooth curve $f(z)$. We prove that for a set of points satisfying the condition $|f(\alpha _{1})- \alpha _{2}|<c_{1}Q^{- \gamma }$ their quantity is bounded below by $c_{15}Q^{n+1- \gamma }$.
Received: 04.06.2018
Document Type: Article
UDC: 511.42
Language: Russian
Citation: V. I. Bernik, M. A. Zhur, “Complex algebraic numbers in the sets of $\mathbb{C}^2$ of small Lebesgue measure”, Tr. Inst. Mat., 26:1 (2018), 25–30
Citation in format AMSBIB
\Bibitem{BerZhu18}
\by V.~I.~Bernik, M.~A.~Zhur
\paper Complex algebraic numbers in the sets of $\mathbb{C}^2$ of small Lebesgue measure
\jour Tr. Inst. Mat.
\yr 2018
\vol 26
\issue 1
\pages 25--30
\mathnet{http://mi.mathnet.ru/timb286}
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