An update on the sum-product problem
| Autor: | Rudnev, Misha, Stevens, Sophie |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Math. Proc. Cambridge Phil. Soc. 2021 |
| Druh dokumentu: | Working Paper |
| Popis: | We improve the best known sum-product estimates over the reals. We prove that \[ \max(|A+A|,|AA|)\geq |A|^{\frac{4}{3} + \frac{2}{1167} - o(1)}\,, \] for a finite $A\subset \mathbb R$, following a streamlining of the arguments of Solymosi, Konyagin and Shkredov. We include several new observations to our techniques. Furthermore, \[ |AA+AA|\geq |A|^{\frac{127}{80} - o(1)}\,. \] Besides, for a convex set $A$ we show that \[ |A+A|\geq |A|^{\frac{30}{19}-o(1)}\,. \] This paper is largely self-contained. Comment: 19 pages, refereed version |
| Databáze: | arXiv |
| Externí odkaz: |
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