4 citations · 7 across the 9 of their papers we have counts for
9 papers
The Distribution of Special Subsets of the Farey Sequence
Alan K. Haynes
In this paper we generalize some of our results from, `A note on Farey fractions with odd denominators' to subsets of Farey fractions consisting of fractions with denominators not…
A Note on Farey Fractions With Odd Denominators
Alan K. Haynes
In this paper we examine the subset of Farey fractions of order Q consisting of those fractions whose denominators are odd. In particular, we consider the frequencies of values of…
A note on Farey fractions with denominators in arithmetic progressions
Dmitry A. Badziahin, Alan K. Haynes
As the conclusion of a line of investigation undertaken in two previous papers, we compute asymptotic frequencies for the values taken by numerators of differences of consecutive F…
Numerators of differences of nonconsecutive Farey fractions
Alan K. Haynes
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…
Intermediate convergents and a metric theorem of Khinchin
Alan K. Haynes
A landmark theorem in the metric theory of continued fractions begins this way: Select a non-negative real function defined on the positive integers and a real number , and…
The group ring of Q/Z and an application of a divisor problem
Alan K. Haynes, Kosuke Homma
First we prove some elementary but useful identities in the group ring of Q/Z. Our identities have potential applications to several unsolved problems which involve sums of Farey f…