English

An improved sum-product estimate over finite fields

Combinatorics 2011-06-07 v1

Abstract

This paper gives an improved sum-product estimate for subsets of a finite field whose order is not prime. It is shown, under certain conditions, that max{A+A,AA}A12/11(log2A)5/11.\max\{|A+A|,|A\cdot{A}|\}\gg{\frac{|A|^{12/11}}{(\log_2|A|)^{5/11}}}. This new estimate matches, up to a logarithmic factor, the current best known bound obtained over prime fields by Rudnev (\cite{mishaSP}).

Keywords

Cite

@article{arxiv.1106.1148,
  title  = {An improved sum-product estimate over finite fields},
  author = {Liangpan Li and Oliver Roche-Newton},
  journal= {arXiv preprint arXiv:1106.1148},
  year   = {2011}
}
R2 v1 2026-06-21T18:18:31.316Z