Positive Limit-Fourier transform of Farey fractions

Products of Farey Fractions

The Correlations of Farey Fractions

We prove that all correlations of the sequence of Farey fractions exist and provide formulas for the correlation measures.

Neighboring Fractions in Farey Subsequences

We present explicit formulas for computation of the neighbors of several elements in Farey subsequences.

Numerators of Differences of Nonconsecutive Farey Fractions

Abstract. An elementary but useful fact is that the numerator of the difference of two consecutive Farey fractions is equal to one. For triples of consecutive fractions the numerators of the differences are well understood and have applications to several interesting problems. In this paper we investigate numerators of differences of fractions which are farther apart. We establish algebraic ide...

Metrical Theory for Farey Continued Fractions

By making fundamental use of the Farey shift map and employing infinite (but σ-finite) measures together with the Chacon-Ornstein ergodic theorem it is possible to find new metrical results for continued fractions. Moreover this offers a unified approach to several existing theorems. The application of ergodic theory to the study of continued fractions began with the Gauss transformation, G: [0...