РЕГУЛЯНОСТЬ РАСПРЕДЕЛЕНИЯ КОМПЛЕКСНЫХ АЛГЕБРАИЧЕСКИХ ЧИСЕЛ В КРУГАХ МАЛОГО РАДИУСА

For any sufficiently large positive integer Q ≥ Q 0 ( n )we prove that there exist complex circles K 1 , K 2 є C of radii r 1 and r 2 , max( r 1 , r 2 ) c 01 ( n ), containing no algebraic numbers αє K 1 , βє K 2 with heights bounded by Q , max( H (α), H (β))≤ Q . We also show that if the radii of the circles K 1 and K 2 obey the condition min( r 1 , r 2 ) > c 2 ( n ) Q -1/4 , c 2 > c 02 ( n ), then the number of algebraic numbers lying in these circles is bounded from below by c 3 ( n ) Q 5 r 1 2 r 2 2 .