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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2015, Volume 290, Pages 304–316
DOI: https://doi.org/10.1134/S0371968515030255 (Mi tm3634) 		 
This article is cited in 42 scientific papers (total in 43 papers)

On sum sets of sets having small product set

S. V. Konyagin, I. D. Shkredov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Full-text PDF (211 kB) Citations (43)
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DOI: https://doi.org/10.1134/S0371968515030255
Abstract: We improve the sum–product result of Solymosi in $\mathbb R$; namely, we prove that $\max \{|A+A|,|AA|\}\gg |A|^{4/3+c}$, where $c>0$ is an absolute constant. New lower bounds for sums of sets with small product set are found. Previous results are improved effectively for sets $A\subset \mathbb R$ with $|AA| \le |A|^{4/3}$.
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 15, 2015
English version:
Proceedings of the Steklov Institute of Mathematics, 2015, Volume 290, Issue 1, Pages 288–299
DOI: https://doi.org/10.1134/S0081543815060255
Bibliographic databases:
Document Type: Article
UDC: 511.178
Language: Russian
Citation: S. V. Konyagin, I. D. Shkredov, “On sum sets of sets having small product set”, Modern problems of mathematics, mechanics, and mathematical physics, Collected papers, Trudy Mat. Inst. Steklova, 290, MAIK Nauka/Interperiodica, Moscow, 2015, 304–316; Proc. Steklov Inst. Math., 290:1 (2015), 288–299
Citation in format AMSBIB
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\pages 304--316
\publ MAIK Nauka/Interperiodica
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    • This publication is cited in the following 43 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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