On the Discretized Sum-Product Problem
Name
1804.02475.pdf
Description
Accepted version
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188.27 KB
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Adobe PDF
Checksum (MD5)
1e812922f935b12f1b0870a58245554e
Author(s)
Guth, Larry
Katz, Nets Hawk
Zahl, Joshua
Date Issued
2020
Journal
International Mathematics Research Notices
Publisher
Oxford University Press (OUP)
Version
Author's final manuscript
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 $A\subset \mathbb {R}$ is a $(\delta ,1/2)_1$-set in the sense of Katz and Tao, then either $A+A$ or $A.A$ must have measure at least $|A|^{1-\frac {1}{68}}$.
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 $(\delta ,1/2)_1$-set in the sense of Katz and Tao, then either $A+A$ or $A.A$ must have measure at least $|A|^{1-\frac {1}{68}}$.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1093/IMRN/RNZ360
