An improved sum-product estimate for general finite fields

Li, L. and Roche-Newton, O. (2011) An improved sum-product estimate for general finite fields. SIAM Journal on Discrete Mathematics, 25 (3). pp. 1285-1296. ISSN 1095-7146 doi: 10.1137/110823122

Abstract/Summary

An improved sum-product estimate for subsets of a finite field whose order is not prime is provided. It is shown, under certain conditions, that max{∣∣∣A+A∣∣∣,∣∣∣A⋅A∣∣∣}≫∣∣A∣∣12/11(log2∣∣A∣∣)5/11. This new estimate matches, up to a logarithmic factor, the current best known bound obtained over prime fields by Rudnev