Szemerédi-type theorems for subsets of locally compact abelian groups of positive upper Banach density
Volume 180 / 2017
Acta Arithmetica 180 (2017), 101-109 MSC: Primary 22B05; 37A15; Secondary 11B25; 37A45. DOI: 10.4064/aa8470-4-2017 Published online: 1 August 2017
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.