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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 $c_{15}Q^{n+1- \gamma }$.
Received: 04.06.2018
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
Linking options:
https://www.mathnet.ru/eng/timb286 https://www.mathnet.ru/eng/timb/v26/i1/p25
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Abstract page: | 63 | Full-text PDF : | 15 | References: | 13 |
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