Long Arithmetic Progressions in Critical Sets

2004/03/03 by Ernie Croot, Croot, Ernie
Mathematics · #05D99 #11P70 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT) #math.CO #math.NT #msc:05D99 #msc:11P70

paper · pdf · doi:10.48550/arxiv.math/0403082

Clarified introduction

arxiv created 2004/03/05 · arxiv updated 2009/12/01

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.

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