  Let $F_n$ denote the distribution function of the normalized sum $Z_n = (X_1
+ \dots + X_n)/\sigma\sqrt{n}$ of i.i.d. random variables with finite fourth
absolute moment. In this paper, polynomial rates of convergence of $F_n$ to the
normal law with respect to the Kolmogorov distance, as well as polynomial
approximations of $F_n$ by the Edgeworth corrections (modulo logarithmically
growing factors in $n$) are given in terms of the characteristic function of
$X_1$. Particular cases of the problem are discussed in connection with
Diophantine approximations.
