Long Arithmetic Progressions in Critical Sets

Ernie Croot

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Long Arithmetic Progressions in Critical Sets

Ernie Croot

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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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Ernie Croot. 2004-03-05. Long Arithmetic Progressions in Critical Sets. https://arxiv.org/abs/math/0403082

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