Finite field models in additive combinatorics

2005/07/21 by Ben Green · 2 citations
Mathematics · Computer Science · Engineering · #Limits and Structures in Graph Theory #Advanced Graph Theory Research #graph theory and CDMA systems

paper · doi:10.1017/cbo9780511734885.002

openalex publication_date 2005/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

Abstract

The study of many problems in additive combinatorics, such as Szemer 'edi's theorem on arithmetic progressions, is made easier by first studying models for the problem in F_pⁿ for some fixed small prime p. We give a number of examples of finite field models of this type, which allows us to introduce some of the central ideas in additive combinatorics relatively cleanly. We also give an indication of how the intuition gained from the study of finite field models can be helpful for addressing the original questions.

Citations

• On Some Sequences of Integers
• On Certain Sets of Integers
• Recent progress on the Kakeya conjecture
• Quasi-random graphs

Cited by

• Green's sumset problem at density one half
• Finite field [wikipedia]