(joint work with Olof Sisask) We present an improvement to Roth’s theorem on arithmetic progressions, by showing that if A ⊂ [N] has no non-trivial three-term arithmetic progressions then |A| ≪ N/(log N)1+c for some positive absolute constant c. In particular, this establishes the first non-trivial case of a conjecture of Erdős on arithmetic progressions.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
