An improved sum-product estimate over finite fields

Details An improved sum-product estimate over finite fields An improved sum-product estimate over finite fields

2011-05-31

arxiv.org/abs/1106.1148v1

Mathematics

Combinatorics

Scientific paper

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
$$\max\{|A+A|,|A\cdot{A}|\}\gg{\frac{|A|^{12/11}}{(\log_2|A|)^{5/11}}}.$$ This
new estimate matches, up to a logarithmic factor, the current best known bound
obtained over prime fields by Rudnev (\cite{mishaSP}).

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