Sumsets in difference sets

DOI10.1007/s11856-009-0100-3zbMath1250.11009OpenAlexW2010014812WikidataQ105942405 ScholiaQ105942405MaRDI QIDQ2655770

Imre Z. Ruzsa, Vitaly Bergelson

Publication date: 26 January 2010

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11856-009-0100-3

zbMATH Keywords

difference settriple productmeasure-preserving transformationspositive upper Banach densitypositive asymptotic densityBohr neighbourhoodtriple summeasure-theoretic methodsnumber of solutions of a linear equationtopology of sets of numbers

Mathematics Subject Classification ID

Measure-preserving transformations (28D05) Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.) (05B10) Density, gaps, topology (11B05) Additive bases, including sumsets (11B13)

Related Items (7)

Bohr neighborhoods in generalized difference sets ⋮ Semicontinuity of structure for small sumsets in compact abelian groups ⋮ Separating Bohr denseness from measurable recurrence ⋮ Bohr sets in sumsets II: countable abelian groups ⋮ Sumsets of dense sets and sparse sets ⋮ On Katznelson’s Question for skew-product systems ⋮ Recurrence, rigidity, and popular differences

Cites Work

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• Large independent sets in shift-invariant graphs
• On Certain Sets of Positive Density
• Sets of Recurrence of Z^m -Actions and Properties of Sets of Differences in Z^m
• Integer Sum Sets Containing Long Arithmetic Progressions
• An ergodic IP polynomial Szemerédi theorem
• Double recurrence and almost sure convergence.
• Polynomial extensions of van der Waerden’s and Szemerédi’s theorems
• Arithmetic progressions in sumsets

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