Geodesic
On large subsets of $\mathbb{F}_q^n$ with no three-term arithmetic progression
Jordan S. Ellenberg1 ; Dion Gijswijt2
1 University of Wisconsin, Madison, WI
2 Delft University of Technology, Delft, The Netherlands
Annals of mathematics, Tome 185 (2017) no. 1, pp. 339-343.

Voir la notice de l'article provenant de la source Annals of Mathematics website

In this note, we show that the method of Croot, Lev, and Pach can be used to bound the size of a subset of $\mathbb{F}_q^n$ with no three terms in arithmetic progression by $c^n$ with $c < q$. For $q=3$, the problem of finding the largest subset of $\mathbb{F}_3^n$ with no three terms in arithmetic progression is called the cap set problem. Previously the best known upper bound for the affine cap problem, due to Bateman and Katz, was on order $n^{-1-\epsilon} 3^n$.
DOI : 10.4007/annals.2017.185.1.8

Jordan S. Ellenberg 1 ; Dion Gijswijt 2

1 University of Wisconsin, Madison, WI
2 Delft University of Technology, Delft, The Netherlands 
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Jordan S. Ellenberg; Dion Gijswijt. On large subsets of $\mathbb{F}_q^n$ with no  three-term arithmetic progression. Annals of mathematics, Tome 185 (2017) no. 1, pp. 339-343. doi : 10.4007/annals.2017.185.1.8. http://geodesic.mathdoc.fr/articles/10.4007/annals.2017.185.1.8/

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