Sum-product estimates in finite fields

Details Sum-product estimates in finite fields Sum-product estimates in finite fields

2006-09-14

arxiv.org/abs/math/0609426v3

Mathematics

Combinatorics

Scientific paper

We prove, using combinatorics and Kloosterman sum technology that if $A
\subset {\Bbb F}_q$, a finite field with $q$ elements, and $q^{{1/2}} \lesssim
|A| \lesssim q^{{7/10}}$, then $\max \{|A+A|, |A \cdot A|\} \gtrsim
\frac{{|A|}^{{3/2}}}{q^{{1/4}}$.

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