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Potential theory of the farthest point distance function

✍ Scribed by Stephen J. Gardiner; Ivan Netuka


Book ID
107526816
Publisher
Springer-Verlag
Year
2007
Tongue
English
Weight
142 KB
Volume
101
Category
Article
ISSN
0021-7670

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Asymptotic Distribution of the Distance
✍ Pavel Kargaev; Anatoly Zhigljavsky πŸ“‚ Article πŸ“… 1997 πŸ› Elsevier Science 🌐 English βš– 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 Γ„ we derive the asymptotic distributions of the functions n 2 \ n (x) and n\ n (x$Γ‚n), 0 x$ n. We also establish the asymptotics for 1 0 \ $ n (x) dx, for all real $