Cristian Cobeli, Marian Vâjâitu and Alexandru Zaharescu: On the intervals of a third between Farey fractions, p.239-250

Abstract:

The spacing distribution between Farey points has drawn attention in recent years. It was found that the gaps $\ga_{j+1}-\ga_j$ between consecutive elements of the Farey sequence produce, as $Q\to\infty$, a limiting measure. Numerical computations suggest that for any $d\ge 2$, the gaps $\ga_{j+d}-\ga_j$ also produce a limiting measure whose support is distinguished by remarkable topological features. Here we prove the existence of the spacing distribution for $d=2$ and characterize completely the corresponding support of the measure.

Key Words: Spacing distribution, Farey fractions.

2000 Mathematics Subject Classification: Primary: 11N37;
Secondary: 11B57.

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