Geodesic
Gowers norms for automatic sequences
Discrete analysis (2023) Cet article a éte moissonné depuis la source Scholastica

Voir la notice de l'article

We show that any automatic sequence can be separated into a structured part and a Gowers uniform part in a way that is considerably more efficient than guaranteed by the Arithmetic Regularity Lemma. For sequences produced by strongly connected and prolongable automata, the structured part is rationally almost periodic, while for general sequences the description is marginally more complicated. In particular, we show that all automatic sequences orthogonal to periodic sequences are Gowers uniform. As an application, we obtain for any $l \geq 2$ and any automatic set $A \subset \mathbb{N}_0$ lower bounds on the number of $l$-term arithmetic progressions - contained in $A$ - with a given difference. The analogous result is false for general subsets of $\mathbb{N}_0$ and progressions of length $\geq 5$.
Publié le : 
@article{DAS_2023_a18,
     author = {Jakub Byszewski and Jakub Konieczny and Clemens M\"ullner},
     title = {Gowers norms for automatic sequences},
     journal = {Discrete analysis},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DAS_2023_a18/}
}
TY  - JOUR
AU  - Jakub Byszewski
AU  - Jakub Konieczny
AU  - Clemens Müllner
TI  - Gowers norms for automatic sequences
JO  - Discrete analysis
PY  - 2023
UR  - http://geodesic.mathdoc.fr/item/DAS_2023_a18/
LA  - en
ID  - DAS_2023_a18
ER  - 
%0 Journal Article
%A Jakub Byszewski
%A Jakub Konieczny
%A Clemens Müllner
%T Gowers norms for automatic sequences
%J Discrete analysis
%D 2023
%U http://geodesic.mathdoc.fr/item/DAS_2023_a18/
%G en
%F DAS_2023_a18
Jakub Byszewski; Jakub Konieczny; Clemens Müllner. Gowers norms for automatic sequences. Discrete analysis (2023). http://geodesic.mathdoc.fr/item/DAS_2023_a18/