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arXiv:math/0607208 [math.NT]AbstractReferencesReviewsResources

On the Structure of Sets with Few Three-Term Arithmetic Progressions

Ernie Croot

Published 2006-07-07Version 1

Fix a density d in (0,1], and let F_p^n be a finite field, where we think of p fixed and n tending to infinity. Let S be any subset of F_p^n having the minimal number of three-term progressions, subject to the constraint |S| is at least dp^n. We show that S must have some structure, and that up to o(p^n) elements, it is a union of a small number of cosets of a subspace of dimension n-o(n).

Comments: This is a much cleaner version of a proof published on the arxives three years ago, but where this one holds for finite fields F_p^n. The result in this paper is much clearer than that published previously
Categories: math.NT
Subjects: 11P70
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