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The distribution of the integers N for which {θN} < φ

Published online by Cambridge University Press:  24 October 2008

N. B. Slater
N. B. Slater
Affiliation:
The UniversityLeeds
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Extract

Let ν(M) denote the number of integers N in the range (0 ≤ N ≤ M) for which

where {y} denotes the fractional part of y. It is a convenient but trivial restriction to assume always that θ and φ lie between 0 and 1. There is a well-known result, which will be called ‘Weyl's Theorem’, that if θ is irrational,

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 46 , Issue 4 , October 1950 , pp. 525 - 534
Copyright
Copyright © Cambridge Philosophical Society 1950

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