Quantitative bounds in the polynomial Szemerédi theorem:The homogeneous case

Prendiville, Sean (2017) Quantitative bounds in the polynomial Szemerédi theorem:The homogeneous case. Discrete Analysis, 2017 (5). pp. 1-34. ISSN 2397-3129

Abstract

We obtain quantitative bounds in the polynomial Szemerédi theorem of Bergelson and Leibman, provided the polynomials are homogeneous and of the same degree. Such configurations include arithmetic progressions with common difference equal to a perfect kth power.