АЛГЕБРАИЧЕСКИЕ ТОЧКИ В КОРОТКИХ ИНТЕРВАЛАХ

For sufficiently large Q there exist the intervals I ⊂ [0,1) of length c 1 ( n ) Q −1  that do not contain algebraic numbers of any degree n and of height H ( P ) ≤ Q.  In this article we have found an condition for intervals I in terms of the Diophatine approximations when the intervals of length c 2 ( n ) Q −γ , γ >1, contain not less than c 3 ( n ) Q n−2γ+1  algebraic numbers α of height H (α) ≤ Q  and degree deg α = n > 2γ -1.