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On the Discretized Sum-Product Problem

Larry Guth, Nets Hawk Katz, Joshua Zahl

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Source: Crossref

Published: Jan 13, 2020

DOI: 10.1093/imrn/rnz360

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Source abstract

Abstract We give a new proof of the discretized ring theorem for sets of real numbers. As a special case, we show that if ARA\subset \mathbb {R} is a (δ,1/2)1(\delta ,1/2)_1-set in the sense of Katz and Tao, then either A+AA+A or A.AA.A must have measure at least A1168|A|^{1-\frac {1}{68}}.

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