A sum-product estimate in fields of prime order

Details A sum-product estimate in fields of prime order A sum-product estimate in fields of prime order

2003-04-16

arxiv.org/abs/math/0304217v1

Mathematics

Number Theory

Scientific paper

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 $\max(|A+A|,|A\cdot A|)\ge
c|A|^{1+\epsilon}$ for some $\epsilon>0$ and c>0. This extends the result of J.
Bourgain, N. Katz, and T. Tao.

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