On the intervals of a third between Farey fractions

Cristian Cobeli, Marian Vâjâitu, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review


The spacing distribution between Farey points has drawn attention in recent years. It was found that the gaps γj+1 -γj between consecutive elements of the Farey sequence produce, as Q →∞, a limiting measure. Numerical computations suggest that for any d ≥ 2, the gaps ~γj+d -γj 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.

Original languageEnglish (US)
Pages (from-to)239-250
Number of pages12
JournalBulletin Mathematique de la Societe des Sciences Mathematiques de Roumanie
Issue number3
StatePublished - 2010


  • Farey fractions
  • Spacing distribution

ASJC Scopus subject areas

  • General Mathematics


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