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

@inproceedings{Stewart2013OnTD,
  title={On the Distribution of Small Denominators in the Farey Series of Order N},
  author={C. L. Stewart},
  year={2013}
}
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]. 
Expected value of the smallest denominator in a random interval of fixed radius
TLDR
It has been known since work of Franel and Landau in the 1920’s that the Riemann hypothesis can be reformulated as a question about the distribution of reduced rationals in the unit interval, and here this work addresses one such problem, which was communicated to us by E. Sander and J. D. Meiss.
Birkhoff averages and rotational invariant circles for area-preserving maps
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