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On the Distribution of Small Denominators in the Farey Series of Order N

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Advances in Combinatorics

Abstract

Let N be a positive integer. The Farey series of order N is the sequence of rationals h/k with h and k coprime and 1 \(\leq {h} \leq {k} \leq {N} \) arranged in increasing order between 0 and 1, see [1].

Research supported in part by the Canada Research Chairs Program and by Grant A3528 from the Natural Sciences and Engineering Research Council of Canada.

In memory of Professor Herb Wilf

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References

  1. C. Cobeli, A. Zaharescu, The Haros-Farey sequence at two hundred years, a survey, Acta Universitatis Apulensis 5 (2003), 1–38.

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  2. R.R. Hall, A note on the Farey series, J. London Math. Soc. 2 (1970), 139–148.

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  3. G.H. Hardy, E.M. Wright, An introduction to the theory of numbers, 5th ed., Oxford, 1979.

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  4. D. Kruyswijk, H.G. Meijer, On small denominators and Farey sequences, Indagtiones Math. 39 (1977), 332–337.

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  5. C.L. Stewart, On a sum associated with the Farey series, Report ZW88, Mathematisch Centrum (1976), 1–11.

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Correspondence to C. L. Stewart .

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Stewart, C.L. (2013). On the Distribution of Small Denominators in the Farey Series of Order N . In: Kotsireas, I., Zima, E. (eds) Advances in Combinatorics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30979-3_15

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