Szemeredi-type theorems for subsets of locally compact abelian groups of positive upper Banach density

2017/04/10 by Xiongping Dai, Dai, Xiongping, Hailan Liang +3
Mathematics · #11B25 #22B05 #37A15 #37A45 #Advanced Topology and Set Theory #Combinatorics (math.CO) #Dynamical Systems (math.DS) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #math.CO #math.DS #msc:11B25 #msc:22B05 #msc:37A15 #msc:37A45

paper · pdf · doi:10.48550/arxiv.1704.02746

11 pages; accepted by Acta Arith

arxiv created 2017/04/10 · openalex publication_date 2017/04/10 · arxiv updated 2017/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By using ergodic theoretic techniques following Hillel Fürstenberg, we prove that measurable subsets of a locally compact abelian group of positive upper density contain Szemerédi-wise configurations defined by an arbitrary compact subset of the group.

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