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Uniform distribution and Hardy fields

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Abstract

Under certain regularity conditions on the growth at infinity of a real functionf (belonging to some Hardy field), asymptotic distribution modulo 1 of the values off is studied. In particular, necessary and sufficient conditions (in terms of the extent to whichf can be approximated by rational polynomals) are provided for the sequence {f(n)} n≥1 to be uniformly distributed or dense modulo 1.

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Authors and Affiliations

  1. Department of Mathematics, Rice University, 77251, Houston, TX, USA

    Michael D. Boshernitzan

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  1. Michael D. Boshernitzan
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Supported in part by NSF-DMS-9003450.

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Boshernitzan, M.D. Uniform distribution and Hardy fields. J. Anal. Math. 62, 225–240 (1994). https://doi.org/10.1007/BF02835955

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  • DOI: https://doi.org/10.1007/BF02835955

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