Long Arithmetic Progressions in Critical Sets
Number Theory
2007-05-23 v2 Combinatorics
Abstract
In this paper we prove: If 0 < d < 1, and p is a sufficiently large prime, then if S is a subset of Z/pZ having the least number of three-term arithmetic progressions among all subsets of Z/pZ having at least dp elements, then S has an arithmetic progression of length at least log^{1/4+o(1)} x.
Cite
@article{arxiv.math/0403082,
title = {Long Arithmetic Progressions in Critical Sets},
author = {Ernie Croot},
journal= {arXiv preprint arXiv:math/0403082},
year = {2007}
}
Comments
Clarified introduction