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This article is cited in 10 scientific papers (total in 10 papers)
Some remarks on sets with small quotient set
I. D. Shkredov Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Abstract:
We prove that for any finite set $A\subset \mathbb{R}$ with $|A/A| \ll |A|$ we have $|A-A| \gg |A|^{5/3 - o(1)}$. We also show that for such sets $|A+A+A| \gg |A|^{2-o(1)}$.
Bibliography: 22 titles.
Keywords:
additive combinatorics, sum-product phenomenon, Erdős-Szemerédi conjecture.
Received: 16.05.2016 and 16.09.2016
Citation:
I. D. Shkredov, “Some remarks on sets with small quotient set”, Sb. Math., 208:12 (2017), 1854–1868
Linking options:
https://www.mathnet.ru/eng/sm8733https://doi.org/10.1070/SM8733 https://www.mathnet.ru/eng/sm/v208/i12/p144
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Abstract page: | 446 | Russian version PDF: | 40 | English version PDF: | 6 | References: | 34 | First page: | 23 |
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