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