Affiliation:
1. Institute of Mathematics of the National Academy of Sciences of Belarus
Abstract
In the metric theory of Diophantine approximations, one of the main problems leading to exact characteristics in the classifications of Mahler and Koksma is to estimate the Lebesgue measure of the points x ∈ B ⊂ I from the interval I such as the inequality | P (x) | < Q-w, w > n, Q >1 for the polynomials P(x) ∈ Z[x], deg P ≤ n, H(P) ≤Q is satisfied. The methods of obtaining estimates are different at different intervals of w change. In this article, at w > n +1 we get the estimate µ B< c1(n) Q – (w-1/n). The best estimate to date was c2(n) Q –(w- n/n).
Publisher
Publishing House Belorusskaya Nauka