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JOURNALS // Proceedings of the Institute of Mathematics of the NAS of Belarus // Archive

Tr. Inst. Mat., 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

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 $c_{15}Q^{n+1- \gamma }$.

UDC: 511.42

Received: 04.06.2018



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