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# A sum-product estimate in fields of prime order

(16 Apr 2003)  Key: citeulike:11867592

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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 $\max(|A+A|,|A⋅ A|)≥ c|A|^1+ε$ for some $ε>0$ and c>0. This extends the result of J. Bourgain, N. Katz, and T. Tao.