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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the fractional parts of $ n/j,$ $ j=o(n)$


Authors: John Isbell and Stephen Schanuel
Journal: Proc. Amer. Math. Soc. 60 (1976), 65-67
MSC: Primary 10H20; Secondary 10K99
MathSciNet review: 0429796
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Abstract: Dirichlet's result that if $ J(n) = o(n)$ but $ {n^{1/2}} = o(J(n))$, the numbers $ n/j$ for $ j = 1, \ldots ,J(n)$ are nearly uniformly distributed modulo 1 (with error $ \to 0$ as $ n \to \infty $) is extended, $ {n^{1/2}}$ being replaced by $ {n^\alpha }$ for any $ \alpha > 0$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1976-0429796-6
PII: S 0002-9939(1976)0429796-6
Keywords: Uniform distribution
Article copyright: © Copyright 1976 American Mathematical Society