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

Volume 180 / 2017

Xiongping Dai, Hailan Liang, Xinjia Tang Acta Arithmetica 180 (2017), 101-109 MSC: Primary 22B05; 37A15; Secondary 11B25; 37A45. DOI: 10.4064/aa8470-4-2017 Published online: 1 August 2017

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.

Authors

  • Xiongping DaiDepartment of Mathematics
    Nanjing University, Nanjing 210093
    People’s Republic of China
    e-mail
  • Hailan LiangDepartment of Mathematics
    Fuzhou University, Fuzhou 350116
    People’s Republic of China
  • Xinjia TangDepartment of Mathematics
    Nanjing University, Nanjing 210093
    People’s Republic of China

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