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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
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 $|AA| \le |A|^{4/3}$.
Received: March 15, 2015
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
Linking options:
https://www.mathnet.ru/eng/tm3634https://doi.org/10.1134/S0371968515030255 https://www.mathnet.ru/eng/tm/v290/p304
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Abstract page: | 487 | Full-text PDF : | 64 | References: | 60 | First page: | 4 |
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