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This article is cited in 34 scientific papers (total in 35 papers)
New results on sums and products in $\mathbb R$
S. V. Konyagin, I. D. Shkredov Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia
Abstract:
We improve previous sum-product estimates in $\mathbb R$; namely, we prove the inequality $\max\{|A+A|,|AA|\}\gg|A|^{4/3+c}$, where $c$ is any number less than $5/9813$. New lower bounds for sums of sets with small product set are found. We also obtain results on the additive and multiplicative energies; in particular, we improve a result of Balog and Wooley.
Received: March 24, 2016
Citation:
S. V. Konyagin, I. D. Shkredov, “New results on sums and products in $\mathbb R$”, Modern problems of mathematics, mechanics, and mathematical physics. II, Collected papers, Trudy Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016, 87–98; Proc. Steklov Inst. Math., 294 (2016), 78–88
Linking options:
https://www.mathnet.ru/eng/tm3733https://doi.org/10.1134/S0371968516030055 https://www.mathnet.ru/eng/tm/v294/p87
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Abstract page: | 490 | Full-text PDF : | 51 | References: | 54 | First page: | 9 |
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