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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Almost-arithmetic progressions and uniform distribution


Author: H. Niederreiter
Journal: Trans. Amer. Math. Soc. 161 (1971), 283-292
MSC: Primary 10.33
MathSciNet review: 0284406
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Abstract: In a recent paper, P. E. O'Neil gave a new criterion for uniform distribution modulo one in terms of almost-arithmetic progressions. We investigate the relation between almost-arithmetic progressions and uniformly distributed sequences from a quantitative point of view. An upper bound for the discrepancy of almost-arithmetic progressions is given which is shown to be best possible. Estimates for more general sequences are also obtained. As an application, we prove a quantitative form of Fejér's theorem on the uniform distributivity of slowly increasing sequences.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1971-0284406-6
PII: S 0002-9947(1971)0284406-6
Keywords: Almost-arithmetic progressions, uniform distribution modulo one, discrepancy, convex programming
Article copyright: © Copyright 1971 American Mathematical Society