Geodesic
Algebraic numbers in the sets of real and complex numbers of small Lebesgue measure
Trudy Instituta matematiki, Tome 24 (2016) no. 2, pp. 37-43 
M. A. Zhur. Algebraic numbers in the sets of real and complex numbers of small Lebesgue measure. Trudy Instituta matematiki, Tome 24 (2016) no. 2, pp. 37-43. http://geodesic.mathdoc.fr/item/TIMB_2016_24_2_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Algebraic numbers of degree $2n$ are investigated. For any $Q \ge {Q_0}\left( n \right)$ we prove that there exist circles $K_1,\cdots ,K_n$ on the complex plane with the radiuses $max(r_i) c_1 Q^{ - 1}$ containing no algebraic numbers of height less then $Q$. We also prove that for $min(r_i) > {c'}_i Q^{ - \frac{1}{2n}}$ circles $K_1,... ,K_n$ contain algebraic numbers and their quantity is bounded below by ${c_{20}}Q^{2n+1}\mu K$.

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