On the Discretized Sum-Product Problem
<jats:title>Abstract</jats:title> <jats:p>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...
| Main Authors: | , , |
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| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Oxford University Press (OUP)
2021
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| Online Access: | https://hdl.handle.net/1721.1/135572 |
| Summary: | <jats:title>Abstract</jats:title>
<jats:p>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 $|A|^{1-\frac {1}{68}}$.</jats:p> |
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