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A sum-product estimate in fields of prime order

S. V. Konyagin
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Abstract

Let q be a prime, A be a subset of a finite field $F=\Bbb Z/q\Bbb Z$, $|A|<\sqrt{|F|}$. We prove the estimate $\max(|A+A|,|A\cdot A|)\ge c|A|^{1+ε}$ for some $ε>0$ and c>0. This extends the result of J. Bourgain, N. Katz, and T. Tao.

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S. V. Konyagin. 2003-04-16. A sum-product estimate in fields of prime order. https://arxiv.org/abs/math/0304217

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