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Metric discrepancy results for alternating geometric progressions

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Abstract

The law of the iterated logarithm for discrepancies of {θ k x} is proved for θ < −1. When θ is not a power root of rational number, the limsup equals to 1/2. When θ is an odd degree power root of rational number, the limsup constants for ordinary discrepancy and star discrepancy are not identical.

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Authors and Affiliations

  1. Department of Mathematics, Kobe University, Rokko, Kobe, 657-8501, Japan

    Katusi Fukuyama

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  1. Katusi Fukuyama
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Correspondence to Katusi Fukuyama.

Additional information

Communicated by J. Schoißengeier.

The author is supported by KAKENHI 24340017 and 21340027.

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Fukuyama, K. Metric discrepancy results for alternating geometric progressions. Monatsh Math 171, 33–63 (2013). https://doi.org/10.1007/s00605-012-0419-4

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  • DOI: https://doi.org/10.1007/s00605-012-0419-4

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