Improved explicit upper bounds for the Cap Set Problem

Zhi Jiang

Published 2021-03-11Version 1

Ellenberg and Gijswijt gave the best known asymptotic upper bound for the cardinality of subsets of $\mathbb F_q^n$ without 3-term arithmetic progressions. We improve this bound by a factor $\sqrt{n}$. In the case $q=3$, we also obtain more explicit upper bounds for the Cap Set Problem.