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

Vitaly Bergelson; Grigori Kolesnik; Manfred Madritsch; Younghwan Son; Robert Tichy

doi:10.1007/s11856-014-1049-4

Uniform distribution of prime powers and sets of recurrence and van der Corput sets in ℤ^k

Vitaly Bergelson^*, Grigori Kolesnik, Manfred Madritsch, Younghwan Son, Robert Tichy

^*Corresponding author for this work

Institute of Analysis and Number Theory (5010)

Research output: Contribution to journal › Article › peer-review

Abstract

We establish new results on sets of recurrence and van der Corput sets in ℤ^k 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.

Original language	English
Pages (from-to)	729-760
Number of pages	32
Journal	Israel Journal of Mathematics
Volume	201
Issue number	2
DOIs	https://doi.org/10.1007/s11856-014-1049-4
Publication status	Published - 2 Oct 2014

ASJC Scopus subject areas

Mathematics(all)

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10.1007/s11856-014-1049-4

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AU - Bergelson, Vitaly

AU - Kolesnik, Grigori

AU - Madritsch, Manfred

AU - Son, Younghwan

AU - Tichy, Robert

PY - 2014/10/2

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N2 - 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.

AB - 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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JO - Israel Journal of Mathematics

JF - Israel Journal of Mathematics

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Uniform distribution of prime powers and sets of recurrence and van der Corput sets in ℤ^k

Abstract

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