Almost-arithmetic progressions and uniform distribution
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- by H. Niederreiter
- Trans. Amer. Math. Soc. 161 (1971), 283-292
- DOI: https://doi.org/10.1090/S0002-9947-1971-0284406-6
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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.References
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Bibliographic Information
- © Copyright 1971 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 161 (1971), 283-292
- MSC: Primary 10.33
- DOI: https://doi.org/10.1090/S0002-9947-1971-0284406-6
- MathSciNet review: 0284406