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Russian Mathematical Surveys, 2021, Volume 76, Issue 6, Pages 1065–1122
DOI: https://doi.org/10.1070/RM10029 (Mi rm10029) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Non-commutative methods in additive combinatorics and number theory

I. D. Shkredov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
English version PDF (961 kB) Citations (3) Russian version article
References:
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DOI: https://doi.org/10.1070/RM10029
Abstract: The survey is devoted to applications of growth in non-Abelian groups to a number of problems in number theory and additive combinatorics. We discuss Zaremba's conjecture, sum-product theory, incidence geometry, the affine sieve, and some other questions.
Bibliography: 149 titles.
Keywords: number theory, additive combinatorics, Zaremba's conjecture, growth in groups, affine sieve.
Funding agency Grant number
Russian Science Foundation 19-11-00001
This work was supported by the Russian Science Foundation under grant no. 19-11-00001.
Received: 06.06.2021
Bibliographic databases:
Document Type: Article
UDC: 511.218+511.336
MSC: Primary 11B30; Secondary 05E16, 11B75, 11J70, 11L07, 20F69
Language: English
Original paper language: Russian
Citation: I. D. Shkredov, “Non-commutative methods in additive combinatorics and number theory”, Russian Math. Surveys, 76:6 (2021), 1065–1122
Citation in format AMSBIB
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\by I.~D.~Shkredov
\paper Non-commutative methods in additive combinatorics and number theory
\jour Russian Math. Surveys
\yr 2021
\vol 76
\issue 6
\pages 1065--1122
\mathnet{http://mi.mathnet.ru/eng/rm10029}
\crossref{https://doi.org/10.1070/RM10029}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4344398}
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\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2021RuMaS..76.1065S}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85129038020}
Linking options:
  • https://www.mathnet.ru/eng/rm10029
  • https://doi.org/10.1070/RM10029
  • https://www.mathnet.ru/eng/rm/v76/i6/p119
    • This publication is cited in the following 3 articles:
    1. Swee Hong Chan, Igor Pak, “Linear extensions and continued fractions”, European Journal of Combinatorics, 122 (2024), 104018  crossref
    2. I. D. Shkredov, “On a girth–free variant of the Bourgain–Gamburd machine”, Finite Fields and Their Applications, 90 (2023), 102225  crossref  mathscinet
    3. M. V. Lyamkin, “Some applications of growth in SL2(FFp) to the proof of modular versions of Zaremba's conjecture”, Sb. Math., 213:10 (2022), 1415–1435  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Успехи математических наук Russian Mathematical Surveys
    Statistics & downloads:
    Abstract page:436
    Russian version PDF:151
    English version PDF:214
    Russian version HTML:71
    References:58
    First page:21
     
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