On metric estimates of approximation properties of monic polynomial values

N. V. Shamukova^ab, N. I. Kalosha<sup>ab

a</sup> Belarusian State Economic University
^b Institute of Mathematics of the National Academy of Sciences of Belarus

Abstract: The cases of convergence are proved in several analogues of Khinchine's theorem for approximation of zero by values of monic integer polynomials, including the case of nonmonotonic functions in the right-hand side of the inequalities and simultaneous approximations in $\mathbb{R}^2$.

UDC: 511.36

Received: 15.10.2012