English

Sum-product estimates in finite fields

Combinatorics 2007-05-23 v3 Classical Analysis and ODEs

Abstract

We prove, using combinatorics and Kloosterman sum technology that if AFqA \subset {\Bbb F}_q, a finite field with qq elements, and q1/2Aq7/10q^{{1/2}} \lesssim |A| \lesssim q^{{7/10}}, then \max \{|A+A|, |A \cdot A|\} \gtrsim \frac{{|A|}^{{3/2}}}{q^{{1/4}}.

Keywords

Cite

@article{arxiv.math/0609426,
  title  = {Sum-product estimates in finite fields},
  author = {D. Hart and A. Iosevich and J. Solymosi},
  journal= {arXiv preprint arXiv:math/0609426},
  year   = {2007}
}