Quantitative bounds in the polynomial Szemerédi theorem: the homogeneous case

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.

v2. Title changed and substantial alterations to exposition. v3. Referee comments incorporated. v4 Formatted using Discrete analysis style file

References in corpus (2)

• A quantitative improvement for Roth's theorem on arithmetic progressions
• Concatenation theorems for anti-Gowers-uniform functions and Host-Kra characteristic factors

Cited by in corpus (6)

• On the polynomial Szemerédi theorem in finite fields
• The inverse theorem for the nonlinear Roth configuration: an exposition
• Bootstrapping partition regularity of linear systems
• Lower bounds in the polynomial Szemerédi theorem
• Further bounds in the polynomial Szemerédi theorem over finite fields
• Bounds in a popular multidimensional nonlinear Roth theorem