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A law of the iterated logarithm for discrepancies: non-constant limsup

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Abstract

We prove the existence of a sequence {n k x} whose discrepancies obey a bounded law of the iterated logarithm with a non-constant limsup.

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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 was supported in part by the Grant-in-Aid for Scientific Research (B) 17340029 from JSPS.

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Fukuyama, K. A law of the iterated logarithm for discrepancies: non-constant limsup. Monatsh Math 160, 143–149 (2010). https://doi.org/10.1007/s00605-008-0062-2

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  • DOI: https://doi.org/10.1007/s00605-008-0062-2

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