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An update on the sum-product problem.
- Source :
-
Mathematical Proceedings of the Cambridge Philosophical Society . Sep2022, Vol. 173 Issue 2, p411-430. 20p. - Publication Year :
- 2022
-
Abstract
- We improve the best known sum-product estimates over the reals. We prove that \[\max(|A+A|,|A+A|)\geq |A|^{\frac{4}{3} + \frac{2}{1167} - o(1)}\,,\] 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. [ABSTRACT FROM AUTHOR]
- Subjects :
- *FINITE, The
*ARGUMENT
Subjects
Details
- Language :
- English
- ISSN :
- 03050041
- Volume :
- 173
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Mathematical Proceedings of the Cambridge Philosophical Society
- Publication Type :
- Academic Journal
- Accession number :
- 158569858
- Full Text :
- https://doi.org/10.1017/S0305004121000633