Long Arithmetic Progressions in Critical Sets

Details Long Arithmetic Progressions in Critical Sets Long Arithmetic Progressions in Critical Sets

2004-03-03

arxiv.org/abs/math/0403082v2

Mathematics

Number Theory

Clarified introduction

Scientific paper

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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