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arXiv · 1804.02475

On the discretized sum-product problem

Larry Guth·Nets Hawk Katz·Joshua Zahl
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Abstract

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

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Larry Guth, Nets Hawk Katz, Joshua Zahl. 2019-12-03. On the discretized sum-product problem. https://doi.org/10.1093/imrn%2Frnz360

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