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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2016, Volume 294, Pages 87–98
DOI: https://doi.org/10.1134/S0371968516030055 (Mi tm3733) 		 
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
Full-text PDF (214 kB) Citations (35)
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DOI: https://doi.org/10.1134/S0371968516030055
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.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.
Received: March 24, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2016, Volume 294, Pages 78–88
DOI: https://doi.org/10.1134/S0081543816060055
Bibliographic databases:
Document Type: Article
UDC: 511.178
Language: Russian
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
Citation in format AMSBIB
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    • This publication is cited in the following 35 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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