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On large subsets of $F_q^n$ with no three-term arithmetic progression by Ellenberg, Jordan S.; Gijswijt, Dion is a scholarly article available to read on EtoBox.

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In this note, we show that the method of Croot, Lev, and Pach can be used to bound the size of a subset of $F_q^n$ with no three terms in arithmetic progression by $c^n$ with $c < q$. For $q=3$, the problem of finding the largest subset with no three terms in arithmetic progression is called the `cap problem'. Previously the best known upper bound for the cap problem, due to Bateman and Katz, was $O(3^n / n^{1+\epsilon})$.

Author

Ellenberg, Jordan S.; Gijswijt, Dion

Published

2016

Language

EN