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An upper estimate for the discrepancy of irrational rotations

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Abstract

We give an upper bound for the discrepancy of irrational rotations \({\{n\alpha\}}\) in terms of the continued fraction expansion of \({\alpha}\) and the related Ostrowski expansion. Our result improves earlier bounds in the literature and substantially simplifies their proofs.

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Authors and Affiliations

  1. Graduate School of Science, Department of Applied Mathematics, Okayama University of Science, 1-1 Ridai-cho, Okayama, 700-0005, Japan

    K. Doi, N. Shimaru & K. Takashima

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  1. K. Doi
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  2. N. Shimaru
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  3. K. Takashima
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Correspondence to K. Takashima.

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Doi, K., Shimaru, N. & Takashima, K. An upper estimate for the discrepancy of irrational rotations. Acta Math. Hungar. 152, 109–113 (2017). https://doi.org/10.1007/s10474-017-0702-x

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  • DOI: https://doi.org/10.1007/s10474-017-0702-x

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