The distribution of special subsets of the Farey sequence
โ Scribed by Alan Haynes
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 218 KB
- Volume
- 107
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
โฆ 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:
๐ SIMILAR VOLUMES
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$รn), 0 x$ n. We also establish the asymptotics for 1 0 \ $ n (x) dx, for all real $
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