On the distribution of index of Farey sequences (Q6196082)

The present research deals with the distribution of index of Farey fractions. The authors note a technique, which was used to prove, as ``providing asymptotic formulas for moments of index of Farey fractions twisted by Dirichlet characters for Farey fractions with \(\mathcal{B}\)-free denominators''. In addition, one can note the following results: the square-free case from \textit{E. Alkan} et al. [Ramanujan J. 16, No. 2, 131--161 (2008; Zbl 1182.11012)] is reconsidered; ``new results for moments of indices with square-free denominators'' and ``higher level correlation measures of the index function'' are obtained. The authors present generalizations of earlier known results on two level correlations, note that the characteristic function of square-free numbers is not completely multiplicative, and correct the corresponding errors, as well as give new estimates on the moments of index function over square-free denominators. The special attention is also given to considerations of results such that are useful to prove the main results of this paper, and to explanations of used techniques.