English

Improved explicit upper bounds for the Cap Set Problem

Combinatorics 2023-01-09 v3 Number Theory

Abstract

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

Keywords

Cite

@article{arxiv.2103.06481,
  title  = {Improved explicit upper bounds for the Cap Set Problem},
  author = {Zhi Jiang},
  journal= {arXiv preprint arXiv:2103.06481},
  year   = {2023}
}
R2 v1 2026-06-23T23:59:09.095Z