The sum-product estimate for large subsets of prime fields

2007/06/05 by M. Z. Garaev, Garaev, M. Z.
Mathematics · #Limits and Structures in Graph Theory #Analytic Number Theory Research #Finite Group Theory Research

paper · pdf · doi:10.48550/arxiv.0706.0702

Abstract

Let \mathbbF_p be the field of a prime order p. It is known that for any integer N∈ [1,p] one can construct a subset A⊂\mathbbF_p with |A|= N such that max\|A+A|, |AA|\≪ p^1/2|A|^1/2. In the present paper we prove that if A⊂ \mathbbF_p with |A|>p^2/3, then max\|A+A|, |AA|\≫ p^1/2|A|^1/2.

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