Solymosi's multiplicative energy bound for complex numbers

Abstract

We extend the recent Solymosi's sum-product estimate for reals to the complex case.

This paper was withdrawn by the authors, after L.Li pointed out that the proof had an error. The claim of the paper in question was given a correct proof in the work "New sum-product type estimates", SIAM J. Discrete. Math. 27 (2013), no.2, 873--990, by Konyagin and Rudnev

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