Improved bound in Roth's theorem on arithmetic progressions

Dirichlet’s Theorem on Arithmetic Progressions

Dirichlet’s Theorem on Arithmetic Progressions

Roth’s Theorem on Arithmetic Progressions

Roth’s Theorem on Arithmetic Progressions

The purpose of this paper is to provide a simple and self-contained exposition of the celebrated Roth's theorem on arithmetic progressions of length three. The original result is proved in [Roth53], while the proof given below is very similar to the exposition of Roth's original argument given in [GRS1990]. Definition. We say that a subset of positive integers A has positive upper density if (1...

Dirichlet’s Theorem on Arithmetic Progressions