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 |
| _version_ | 1826191991029891072 |
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| author | Guth, Larry Katz, Nets Hawk Zahl, Joshua |
| author2 | Massachusetts Institute of Technology. Department of Mathematics |
| author_facet | Massachusetts Institute of Technology. Department of Mathematics Guth, Larry Katz, Nets Hawk Zahl, Joshua |
| author_sort | Guth, Larry |
| collection | MIT |
| description | <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> |
| first_indexed | 2024-09-23T09:04:29Z |
| format | Article |
| id | mit-1721.1/135572 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T09:04:29Z |
| publishDate | 2021 |
| publisher | Oxford University Press (OUP) |
| record_format | dspace |
| spelling | mit-1721.1/1355722023-02-17T20:27:33Z On the Discretized Sum-Product Problem Guth, Larry Katz, Nets Hawk Zahl, Joshua Massachusetts Institute of Technology. Department of Mathematics <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> 2021-10-27T20:24:04Z 2021-10-27T20:24:04Z 2020 2021-05-20T14:23:36Z Article http://purl.org/eprint/type/JournalArticle https://hdl.handle.net/1721.1/135572 en 10.1093/IMRN/RNZ360 International Mathematics Research Notices Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/ application/pdf Oxford University Press (OUP) arXiv |
| spellingShingle | Guth, Larry Katz, Nets Hawk Zahl, Joshua On the Discretized Sum-Product Problem |
| title | On the Discretized Sum-Product Problem |
| title_full | On the Discretized Sum-Product Problem |
| title_fullStr | On the Discretized Sum-Product Problem |
| title_full_unstemmed | On the Discretized Sum-Product Problem |
| title_short | On the Discretized Sum-Product Problem |
| title_sort | on the discretized sum product problem |
| url | https://hdl.handle.net/1721.1/135572 |
| work_keys_str_mv | AT guthlarry onthediscretizedsumproductproblem AT katznetshawk onthediscretizedsumproductproblem AT zahljoshua onthediscretizedsumproductproblem |