Progression-free sets in Z_4^n are exponentially small

By Ernie Croot, Vsevolod F. Lev, Péter Pál Pach. 2016

150 citations recorded by the source corpus.

We show that for integer $n>0$, any subset $A \subset Z_4^n$ free of three-term arithmetic progressions has size $|A| < 4^{c n}$, with an absolute constant $c \approx 0.926$.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/58b36bb9743c834e5a7caf904bd0bd02c6efd389

Citations in the corpus

• Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions. (2020, unknown): “Furthermore, as mentioned in the introduction, the new polynomial method by Croot, Lev, and Pach [9] has allowed Ellenberg and Gijswijt [12] to prove bounds for the quantity analogous to r(N) over Fn3 corresponding to (16) with c = 1.”