On the Structure of Sets with Few Three-Term Arithmetic Progressions
数论
2007-05-23 v1
摘要
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).
引用
@article{arxiv.math/0607208,
title = {On the Structure of Sets with Few Three-Term Arithmetic Progressions},
author = {Ernie Croot},
journal= {arXiv preprint arXiv:math/0607208},
year = {2007}
}
备注
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