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NUMERATORS OF DIFFERENCES OF NONCONSECUTIVE FAREY FRACTIONS

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JournalInternational Journal of Number Theory
DatePublished - May 2010
Issue number3
Volume6
Number of pages12
Pages (from-to)655-666
Original languageEnglish

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 identities between such differences which then allow us to calculate their average values by using properties of a measure preserving transformation of the Farey triangle.

    Research areas

  • Farey fractions

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