On some uniformly distributed subsets of rationals (Q6622511)

The paper under review concerns with sets \(\mathcal{S}\subset\mathbb{Q}^+\) such that \(\mathcal{S}=f^{-1}(g)\) with \(g\) to be a value of arithmetical function \(f\) defined on \(\mathbb{Q}^+\). The author first shows uniformity of distribution of elements of \(\mathcal{S}\). Because of relation to the rational numbers, the author interprets uniformity results in sense of Diophantine approximations. More precisely, by using a result due to \textit{G. Harman} [Acta Arith. 53, No. 2, 207--216 (1989; Zbl 0693.10037)] he obtains a variation of Khintchine's theorem in the metrical theory of Diophantine approximations.