A Szemeredi type theorem for sets of positive density in approximate lattices
Artikel i vetenskaplig tidskrift, 2024

An extension of Szemeredi'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 Szemer & eacute;di 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].

Szemeredi's theorem

approximate lattice

cut-and-project sets

Författare

Michael Björklund

Chalmers, Matematiska vetenskaper, Analys och sannolikhetsteori

Alexander Fish

The University of Sydney

Ergodic Theory and Dynamical Systems

0143-3857 (ISSN) 1469-4417 (eISSN)

Vol. In Press

Långväga beroende inom punktprocesser av aritmetiskt ursprung

Vetenskapsrådet (VR) (2023-03803), 2024-01-01 -- 2027-12-31.

Ämneskategorier (SSIF 2011)

Algebra och logik

Matematisk analys

DOI

10.1017/etds.2024.128

Mer information

Senast uppdaterat

2025-01-10