Sumsets in difference sets

Vitaly Bergelson, I. Ruzsa

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We study some properties of sets of differences of dense sets in ℤ2 and ℤ3 and their interplay with Bohr neighbourhoods in ℤ. We obtain, inter alia, the following results. (i) If E ⊂ ℤ2, d̄(E) > 0 and pi, qi ∈ ℤ[x], i = 1, ..., m satisfy pi(0) = qi(0) = 0, then there exists B ⊂ ℤ such that d̄(B) > 0 and, (ii) If A ⊂ ℤ with d̄(A) > 0, then for any r, s, t such that r + s + t = 0 the set rA + sA + tA is a Bohr neighbourhood of 0. (iii) For any 0 <α <1/2 there exists a set E ⊂ ℤ3 with d̄(E) > 0 such that E - E does not contain a set of the form B × B × B, where B ⊂ ℤ and d̄(B) > 0.

Original languageEnglish
Pages (from-to)1-18
Number of pages18
JournalIsrael Journal of Mathematics
Volume174
Issue number1
DOIs
Publication statusPublished - Jan 2010

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Sumsets
Difference Set
Pi
Property of set

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Sumsets in difference sets. / Bergelson, Vitaly; Ruzsa, I.

In: Israel Journal of Mathematics, Vol. 174, No. 1, 01.2010, p. 1-18.

Research output: Contribution to journalArticle

Bergelson, Vitaly ; Ruzsa, I. / Sumsets in difference sets. In: Israel Journal of Mathematics. 2010 ; Vol. 174, No. 1. pp. 1-18.
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