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The distribution of special subsets of the Farey sequence

โœ Scribed by Alan Haynes


Publisher
Elsevier Science
Year
2004
Tongue
English
Weight
218 KB
Volume
107
Category
Article
ISSN
0022-314X

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โœฆ Synopsis


We will examine the subset F Q;p of Farey fractions of order Q consisting of those fractions whose denominators are not divisible by a fixed prime p: In particular, we will provide an asymptotic result on the distribution of H-tuples of consecutive fractions in F Q;p ; as Q-N:


๐Ÿ“œ SIMILAR VOLUMES


The distribution of Farey points
โœ H. Niederreiter ๐Ÿ“‚ Article ๐Ÿ“… 1973 ๐Ÿ› Springer ๐ŸŒ English โš– 185 KB
Asymptotic Distribution of the Distance
โœ Pavel Kargaev; Anatoly Zhigljavsky ๐Ÿ“‚ Article ๐Ÿ“… 1997 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 337 KB

Let x be a real number in [0, 1], F n be the Farey sequence of order n and \ n (x) be the distance between x and F n . Assuming that n ร„ we derive the asymptotic distributions of the functions n 2 \ n (x) and n\ n (x$ร‚n), 0 x$ n. We also establish the asymptotics for 1 0 \ $ n (x) dx, for all real $

The parity of Farey denominators and the
โœ R.R. Hall ๐Ÿ“‚ Article ๐Ÿ“… 2005 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 155 KB

A function E(b, s) is defined on the set {s in N, b in Z, (b, s)=1} implicitly, by a functional equation. Various conjectures arise from tables and some of these are proved. This function is then related to a partial sum of Farey indices weighted according to the parity of the Farey denominators. An