Sbornik: Mathematics
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Mat. Sb.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

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)
References:
PDF
HTML
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
Russian version:
Matematicheskii Sbornik, 2017, Volume 208, Number 12, Pages 144–158
DOI: https://doi.org/10.4213/sm8733
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”, Mat. Sb., 208:12 (2017), 144–158; Sb. Math., 208:12 (2017), 1854–1868
Citation in format AMSBIB
\Bibitem{Shk17}
\by I.~D.~Shkredov
\paper Some remarks on sets with small quotient set
\jour Mat. Sb.
\yr 2017
\vol 208
\issue 12
\pages 144--158
\mathnet{http://mi.mathnet.ru/sm8733}
\crossref{https://doi.org/10.4213/sm8733}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3733364}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2017SbMat.208.1854S}
\elib{https://elibrary.ru/item.asp?id=30738019}
\transl
\jour Sb. Math.
\yr 2017
\vol 208
\issue 12
\pages 1854--1868
\crossref{https://doi.org/10.1070/SM8733}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000425457000006}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042641029}
Linking options:
  • https://www.mathnet.ru/eng/sm8733
  • https://doi.org/10.1070/SM8733
  • https://www.mathnet.ru/eng/sm/v208/i12/p144
    • This publication is cited in the following 10 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:441
    Russian version PDF:40
    English version PDF:4
    References:34
    First page:23
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024