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Uspekhi Mat. Nauk, 2006, Volume 61, Issue 6(372), Pages 111–178 (Mi umn5293)  

This article is cited in 7 scientific papers (total in 7 papers)

Szemerédi's theorem and problems on arithmetic progressions

I. D. Shkredov

M. V. Lomonosov Moscow State University

Abstract: Szemerédi's famous theorem on arithmetic progressions asserts that every subset of integers of positive asymptotic density contains arithmetic progressions of arbitrary length. His remarkable theorem has been developed into a major new area of combinatorial number theory. This is the topic of the present survey.

DOI: https://doi.org/10.4213/rm5293

Full text: PDF file (1138 kB)
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English version:
Russian Mathematical Surveys, 2006, 61:6, 1101–1166

Bibliographic databases:

UDC: 511.218+511.336
MSC: Primary 11B25; Secondary 05D10, 28D05, 28D15
Received: 27.03.2006

Citation: I. D. Shkredov, “Szemerédi's theorem and problems on arithmetic progressions”, Uspekhi Mat. Nauk, 61:6(372) (2006), 111–178; Russian Math. Surveys, 61:6 (2006), 1101–1166

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. D. A. Shabanov, “On the Lower Bound for van der Waerden Functions”, Math. Notes, 87:6 (2010), 918–920  mathnet  crossref  crossref  mathscinet  isi  elib
    2. I. D. Shkredov, “Fourier analysis in combinatorial number theory”, Russian Math. Surveys, 65:3 (2010), 513–567  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    3. D. A. Shabanov, “Van der Waerden's function and colourings of hypergraphs”, Izv. Math., 75:5 (2011), 1063–1091  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. A. M. Raigorodskii, D. A. Shabanov, “The Erdős–Hajnal problem of hypergraph colouring, its generalizations, and related problems”, Russian Math. Surveys, 66:5 (2011), 933–1002  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. D. A. Shabanov, “Van der Waerden function and colorings of hypergraphs with large girth”, Dokl. Math, 88:1 (2013), 473  crossref  mathscinet  zmath  isi  elib  scopus
    6. I. D. Shkredov, “Structure theorems in additive combinatorics”, Russian Math. Surveys, 70:1 (2015), 113–163  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. A. S. Semchenkov, “Maximal Subsets Free of Arithmetic Progressions in Arbitrary Sets”, Math. Notes, 102:3 (2017), 396–402  mathnet  crossref  crossref  mathscinet  isi  elib
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