Open AccessDiophantine approximation with the constant right-hand side of inequalities on short intervals
Author(s) -
В. И. Берник,
Denis Vasilyev,
E. V. Zasimovich
Publication year - 2021
Publication title -
doklady nacionalʹnoj akademii nauk belarusi
Language(s) - English
Resource type - Journals
eISSN - 2524-2431
pISSN - 1561-8323
DOI - 10.29235/1561-8323-2021-65-4-397-403
Subject(s) - mathematics , lebesgue measure , diophantine approximation , diophantine equation , combinatorics , lebesgue integration , interval (graph theory) , constant (computer programming) , measure (data warehouse) , metric (unit) , discrete mathematics , operations management , database , computer science , economics , programming language
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) | 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< c 1 (n) Q – ( w - 1 / n ). The best estimate to date was c 2 (n) Q – ( w -n / n ).