On Roth's theorem on progressions

By Tom Sanders. 2010

186 citations recorded by the source corpus.

We show that if Af 1;:::;Ng contains no nontrivial three-term arithmetic progressions thenjAj = O(N=log 1 o(1) N).

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

View Paper: https://www.semanticscholar.org/paper/b105b1d5ad7035014bd903145251a08e2220a237

Citations in the corpus

• A transference approach to a Roth-type theorem in the squares (2015, unknown): “ Ys i=1 ν(xi). The indicator function of an interval provides an important example of a c-pseudorandom majorant, as can be seen from the following result of Bloom [Blo12] (building on work of Sanders [San11]). Bloom’s theorem ([Blo12]). Let c 1,...,cs ∈ Z\ {0} with s > 3 and c 1+···+cs = 0. Then ”
• Breaking the logarithmic barrier in Roth's theorem on arithmetic progressions. (2020, unknown): “Using regularity in this way is a recurring feature in the works of Bourgain [6, 7] and Sanders [20, 21].”