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Izv. RAN. Ser. Mat., 2006, Volume 70, Issue 2, Pages 179–221 (Mi izv912)  

This article is cited in 12 scientific papers (total in 12 papers)

On a problem of Gowers

I. D. Shkredov

M. V. Lomonosov Moscow State University

Abstract: We prove that every set $A\subseteq\{1,…,N\}^2$ of cardinality at least $\delta N^2$ contains a triple of the form $\{(k,m),(k+d,m),(k,m+d)\}$, where $d>0$, $\delta>0$ is any real number, $N$ is a positive integer, $N\ge \exp\exp\exp\{\delta^{-c}\}$, and $c>0$ is an effective constant.

DOI: https://doi.org/10.4213/im912

Full text: PDF file (756 kB)
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English version:
Izvestiya: Mathematics, 2006, 70:2, 385–425

Bibliographic databases:

UDC: 511.218, 511.336
MSC: 11B25, 05D10, 11L07, 37C25, 37B20, 37A05, 28D05
Received: 15.06.2004

Citation: I. D. Shkredov, “On a problem of Gowers”, Izv. RAN. Ser. Mat., 70:2 (2006), 179–221; Izv. Math., 70:2 (2006), 385–425

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. I. D. Shkredov, “Szemerédi's theorem and problems on arithmetic progressions”, Russian Math. Surveys, 61:6 (2006), 1101–1166  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. Shkredov I.D., “On a generalization of Szemeredi's theorem”, Proceedings of the London Mathematical Society, 93:Part 3 (2006), 723–760  crossref  mathscinet  zmath  isi  elib  scopus
    3. Gowers W. T., “Hypergraph regularity and the multidimensional Szemeredi theorem”, Ann. of Math. (2), 166:3 (2007), 897–946  crossref  mathscinet  zmath  isi  scopus
    4. I. D. Shkredov, “On a two-dimensional analogue of Szemerédi's theorem in Abelian groups”, Izv. Math., 73:5 (2009), 1033–1075  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. 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
    6. Kovac V., “Bellman Function Technique for Multilinear Estimates and an Application to Generalized Paraproducts”, Indiana Univ. Math. J., 60:3 (2011), 813–846  crossref  mathscinet  zmath  isi  elib  scopus
    7. None None, “A new proof of the density Hales-Jewett theorem”, Ann. Math, 175:3 (2012), 1283  crossref  mathscinet  isi  scopus
    8. I. D. Shkredov, “On the Gowers Norms of Certain Functions”, Math. Notes, 92:4 (2012), 554–569  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    9. Sanders T., “Approximate Groups and Doubling Metrics”, Math. Proc. Camb. Philos. Soc., 152:Part 3 (2012), 385–404  crossref  mathscinet  zmath  isi  elib  scopus
    10. Kovac V., “Boundedness of the Twisted Paraproduct”, Rev. Mat. Iberoam., 28:4 (2012), 1143–1164  crossref  mathscinet  zmath  isi  elib  scopus
    11. Anil Ada, Arkadev Chattopadhyay, Omar Fawzi, Phuong Nguyen, “The NOF Multiparty Communication Complexity of Composed Functions”, comput. complex, 2014  crossref  mathscinet  scopus
    12. Durcik P., Kovac V., Rimanic L., “On Side Lengths of Corners in Positive Density Subsets of the Euclidean Space”, Int. Math. Res. Notices, 2018, no. 22, 6844–6869  crossref  mathscinet  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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