Abstract
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 n q Fqn
with no three terms in arithmetic progression by c n cn
with c<q c<q
. For q=3 q=3
, the problem of finding the largest subset of F n 3 F3n
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−ϵ 3 n n−1−ϵ3n
.
Original language | English |
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Pages (from-to) | 339-343 |
Number of pages | 5 |
Journal | Annals of Mathematics |
Volume | 185 |
Issue number | 1 |
DOIs | |
Publication status | Published - 2017 |
Bibliographical note
Accepted author manuscriptKeywords
- additive combinatorics
- additive number theory
- arithmetic progressions
- cap sets