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Uspekhi Mat. Nauk, 2010, Volume 65, Issue 3(393), Pages 127–184 (Mi umn9355)  

This article is cited in 4 scientific papers (total in 4 papers)

Fourier analysis in combinatorial number theory

I. D. Shkredov

M. V. Lomonosov Moscow State University

Abstract: In this survey applications of harmonic analysis to combinatorial number theory are considered. Discussion topics include classical problems of additive combinatorics, colouring problems, higher-order Fourier analysis, theorems about sets of large trigonometric sums, results on estimates for trigonometric sums over subgroups, and the connection between combinatorial and analytic number theory.
Bibliography: 162 titles.

Keywords: Fourier analysis, combinatorial number theory, additive combinatorics.

DOI: https://doi.org/10.4213/rm9355

Full text: PDF file (1173 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 2010, 65:3, 513–567

Bibliographic databases:

UDC: 511.218
MSC: Primary 11B25, 11B75, 42B99; Secondary 05B10, 11B13, 11L07, 11N13, 11P70, 11T23
Received: 07.10.2009

Citation: I. D. Shkredov, “Fourier analysis in combinatorial number theory”, Uspekhi Mat. Nauk, 65:3(393) (2010), 127–184; Russian Math. Surveys, 65:3 (2010), 513–567

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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. Chapman J., Prendiville S., “On the Ramsey Number of the Brauer Configuration”, Bull. London Math. Soc.  crossref  mathscinet  isi
    2. 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
    3. Sanders T., “Bootstrapping Partition Regularity of Linear Systems”, Proc. Edinb. Math. Soc., 63:3 (2020), PII S0013091520000048, 630–653  crossref  mathscinet  isi
    4. K. I. Olmezov, “An Elementary Analog of the Operator Method in Additive Combinatorics”, Math. Notes, 109:1 (2021), 110–119  mathnet  crossref  crossref  mathscinet  isi
  • Успехи математических наук Russian Mathematical Surveys
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