Finite field models in additive combinatorics

Details Finite field models in additive combinatorics Finite field models in additive combinatorics

2004-09-22

arxiv.org/abs/math/0409420v1

Mathematics

Number Theory

24 page survey article, submitted to Surveys in Combinatorics 2005. There are two supplementary documents, containing some pro

Scientific paper

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_p^n 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.

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