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].

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.Expand

Abstract Rotational invariant circles of area-preserving maps are an important and well-studied example of KAM tori. John Greene conjectured that the locally most robust rotational circles have… Expand

Let be the set of representatives for the nonnegative subunitary rational numbers in their lowest terms with denominators at most and arranged in ascending order. This finite sequence of fractions… Expand

THIS book must be welcomed most warmly into X the select class of Oxford books on pure mathematics which have reached a second edition. It obviously appeals to a large class of mathematical readers.… Expand