Year: 2024
Type: article
Abstract: An extension of Szemerédi’s theorem is proved for sets of positive density in approximate lattices in general locally compact and second countable abelian groups. As a consequence, we establish a recent conjecture of Klick, Strungaru and Tcaciuc. Via a novel version of Furstenberg’s correspondence principle, which should be of independent interest, we show that our Szemerédi theorems can be deduced from a general transverse multiple recurrence theorem, which we establish using a recent work of Austin [Non-conventional ergodic averages for several commuting actions of an amenable group. J. Anal. Math.130 (2016), 243–274].
Authors: MICHAEL BJÖRKLUND, ALEXANDER FISH
Institutions: Chalmers University of Technology, The University of Sydney
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,450
OpenAlex ID: W4405694046