On the fractional parts of $n/j,$ $j=o(n)$
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- by John Isbell and Stephen Schanuel PDF
- Proc. Amer. Math. Soc. 60 (1976), 65-67 Request permission
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
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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 10.1007/BF01186558
- Arnold Walfisz, Weylsche Exponentialsummen in der neueren Zahlentheorie, Mathematische Forschungsberichte, XV, VEB Deutscher Verlag der Wissenschaften, Berlin, 1963 (German). MR 0220685
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 60 (1976), 65-67
- MSC: Primary 10H20; Secondary 10K99
- DOI: https://doi.org/10.1090/S0002-9939-1976-0429796-6
- MathSciNet review: 0429796