Geodesic
Three-term arithmetic progressions in subsets of F_q^∞ of large Fourier dimension
Robert Fraser1
1 University of Edinburgh, School of Mathematics
Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 1007-1030.

Voir la notice de l'article provenant de la source Journal.fi

We show that subsets of $\mathbf{F}_q^{\infty}$ of large Fourier dimension must contain three-term arithmetic progressions. This contrasts with a construction of Shmerkin of a subset of $\mathbf{R}$ of Fourier dimension 1 with no three-term arithmetic progressions.
Keywords: Fourier dimension, three-term arithmetic progressions, Fourier analysis, additive combinatorics

Robert Fraser 1

1 University of Edinburgh, School of Mathematics 
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Robert Fraser. Three-term arithmetic progressions in subsets of F_q^∞ of large Fourier dimension. Annales Fennici Mathematici, Tome 46 (2021) no. 2, pp. 1007-1030. http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a23/