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Sbornik: Mathematics, 2017, Volume 208, Issue 12, Pages 1854–1868
DOI: https://doi.org/10.1070/SM8733 (Mi sm8733) 		 
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
English version PDF (516 kB) Citations (10) Russian version article
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DOI: https://doi.org/10.1070/SM8733
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.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant no. 14-50-00005.
Received: 16.05.2016 and 16.09.2016
Bibliographic databases:
Document Type: Article
UDC: 511.218
MSC: 11B75
Language: English
Original paper language: Russian
Citation: I. D. Shkredov, “Some remarks on sets with small quotient set”, Sb. Math., 208:12 (2017), 1854–1868
Citation in format AMSBIB
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\paper Some remarks on sets with small quotient set
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\pages 1854--1868
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    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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