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 
@article{AFM_2021_46_2_a23,
     author = {Robert Fraser},
     title = {Three-term arithmetic progressions in subsets of {F_q^\ensuremath{\infty}} of large {Fourier} dimension},
     journal = {Annales Fennici Mathematici},
     pages = {1007--1030},
     publisher = {mathdoc},
     volume = {46},
     number = {2},
     year = {2021},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a23/}
}
TY  - JOUR
AU  - Robert Fraser
TI  - Three-term arithmetic progressions in subsets of F_q^∞ of large Fourier dimension
JO  - Annales Fennici Mathematici
PY  - 2021
SP  - 1007
EP  - 1030
VL  - 46
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a23/
LA  - en
ID  - AFM_2021_46_2_a23
ER  - 
%0 Journal Article
%A Robert Fraser
%T Three-term arithmetic progressions in subsets of F_q^∞ of large Fourier dimension
%J Annales Fennici Mathematici
%D 2021
%P 1007-1030
%V 46
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AFM_2021_46_2_a23/
%G en
%F AFM_2021_46_2_a23
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/