On the Intervals of a Third between Farey Fractions

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The spacing distribution between Farey points has drawn attention in recent years. It was found that the gaps $γ_{j+1}-γ_j$ 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 $γ_{j+d}-γ_j$ 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.
12 pages, one figure

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Number Theory, 11N37 (primary), 11BB57 (secondary)

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http://salesiana.dossiersoluciones.com/handle/123456789/104921

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0511363
 http://arxiv.org/abs/math/0511363

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arXiv