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Uniform distribution of prime powers and sets of recurrence and van der Corput sets in ℤk

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Abstract

We establish new results on sets of recurrence and van der Corput sets in ℤk which refine and unify some of the previous results obtained by Sárkőzy, Furstenberg, Kamae and Mèndes France, and Bergelson and Lesigne. The proofs utilize a general equidistribution result involving prime powers which is of independent interest.

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Author notes

  1. Younghwan Son

    Present address: Faculty of Mathematics and Computer Science, Weizmann Institute of Science, Rehovot, 76100, Israel

Authors and Affiliations

  1. Department of Mathematics, Ohio State University, Columbus, Ohio, 43210, USA

    Vitaly Bergelson & Younghwan Son

  2. Department of Mathematics, California State University, Los Angeles, CA, 90032, USA

    Grigori Kolesnik

  3. Department for Analysis and Computational Number Theory, Graz University of Technology, A-8010, Graz, Austria

    Manfred Madritsch & Robert Tichy

Authors
  1. Vitaly Bergelson
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  2. Grigori Kolesnik
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  3. Manfred Madritsch
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  4. Younghwan Son
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  5. Robert Tichy
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Corresponding author

Correspondence to Vitaly Bergelson.

Additional information

The first author gratefully acknowledges the support of the NSF under grant DMS-1162073.

The last author gratefully acknowledges the support of the FWF under grant p26114.

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Bergelson, V., Kolesnik, G., Madritsch, M. et al. Uniform distribution of prime powers and sets of recurrence and van der Corput sets in ℤk . Isr. J. Math. 201, 729–760 (2014). https://doi.org/10.1007/s11856-014-1049-4

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  • DOI: https://doi.org/10.1007/s11856-014-1049-4

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