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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 $\alpha > 0$.

References [Enhancements On Off] (What's this?)

    L. E. Dickson, History of the theory of numbers, vol. I, Stechert, New York, 1934.
  • Arnold Walfisz, Über Gitterpunkte in mehrdimensionalen Ellipsoiden, Math. Z. 35 (1932), no. 1, 212–229 (German). MR 1545298, DOI
  • Arnold Walfisz, Weylsche Exponentialsummen in der neueren Zahlentheorie, Mathematische Forschungsberichte, XV, VEB Deutscher Verlag der Wissenschaften, Berlin, 1963 (German). MR 0220685

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Keywords: Uniform distribution
Article copyright: © Copyright 1976 American Mathematical Society