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)

Access to Document

10.1007/s11856-014-1049-4

Cite this

@article{807c4abaa1d44317b7f4af9e52680aa5,

title = "Uniform distribution of prime powers and sets of recurrence and van der Corput sets in ℤ k",

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 S{\'a}rk{\H o}zy, Furstenberg, Kamae and M{\`e}ndes France, and Bergelson and Lesigne. The proofs utilize a general equidistribution result involving prime powers which is of independent interest.",

author = "Vitaly Bergelson and Grigori Kolesnik and Manfred Madritsch and Younghwan Son and Robert Tichy",

year = "2014",

month = oct,

day = "2",

doi = "10.1007/s11856-014-1049-4",

language = "English",

volume = "201",

pages = "729--760",

journal = "Israel journal of mathematics",

issn = "0021-2172",

publisher = "Springer New York",

number = "2",

}

TY - JOUR

T1 - Uniform distribution of prime powers and sets of recurrence and van der Corput sets in ℤ k

AU - Bergelson, Vitaly

AU - Kolesnik, Grigori

AU - Madritsch, Manfred

AU - Son, Younghwan

AU - Tichy, Robert

PY - 2014/10/2

Y1 - 2014/10/2

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.

UR - http://www.scopus.com/inward/record.url?scp=84908542898&partnerID=8YFLogxK

U2 - 10.1007/s11856-014-1049-4

DO - 10.1007/s11856-014-1049-4

M3 - Article

AN - SCOPUS:84908542898

VL - 201

SP - 729

EP - 760

JO - Israel journal of mathematics

JF - Israel journal of mathematics

SN - 0021-2172

IS - 2

ER -

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

Abstract

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this