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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
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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
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Linking options:
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  • https://doi.org/10.1070/RM10029
  • https://www.mathnet.ru/eng/rm/v76/i6/p119
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Успехи математических наук Russian Mathematical Surveys
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    Abstract page:366
    Russian version PDF:132
    English version PDF:123
    Russian version HTML:71
    References:49
    First page:21
     
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