A Szemerédi type theorem for sets of positive density in approximate lattices
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866908400857645056 |
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| author | Björklund, Michael Fish, Alexander |
| author_facet | Björklund, Michael Fish, Alexander |
| contents | 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 \emph{transverse} multiple recurrence theorem, which we establish using recent works of Austin. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_17158 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Szemerédi type theorem for sets of positive density in approximate lattices Björklund, Michael Fish, Alexander Dynamical Systems Combinatorics Number Theory 11B30, 22D40, 05D10 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 \emph{transverse} multiple recurrence theorem, which we establish using recent works of Austin. |
| title | A Szemerédi type theorem for sets of positive density in approximate lattices |
| topic | Dynamical Systems Combinatorics Number Theory 11B30, 22D40, 05D10 |
| url | https://arxiv.org/abs/2402.17158 |