Let be polynomials with distinct degrees, each having zero constant term. We show that any subset A of with no nontrivial progressions of the form has size. Along the way, we prove a general result controlling weighted counts of polynomial progressions by Gowers norms.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Statistics and Probability
- Mathematical Physics
- Geometry and Topology
- Discrete Mathematics and Combinatorics
- 2020 Mathematics Subject Classification