Russian Mathematical Surveys
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Uspekhi Mat. Nauk:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Russian Mathematical Surveys, 2010, Volume 65, Issue 3, Pages 513–567
DOI: https://doi.org/10.1070/RM2010v065n03ABEH004681 (Mi rm9355) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Fourier analysis in combinatorial number theory

I. D. Shkredov

M. V. Lomonosov Moscow State University
English version PDF (879 kB) Citations (5) Russian version article
References:
PDF
HTML
DOI: https://doi.org/10.1070/RM2010v065n03ABEH004681
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.
Received: 07.10.2009
Bibliographic databases:
Document Type: Article
UDC: 511.218
MSC: Primary 11B25, 11B75, 42B99; Secondary 05B10, 11B13, 11L07, 11N13, 11P70, 11T23
Language: English
Original paper language: Russian
Citation: I. D. Shkredov, “Fourier analysis in combinatorial number theory”, Russian Math. Surveys, 65:3 (2010), 513–567
Citation in format AMSBIB
\Bibitem{Shk10}
\by I.~D.~Shkredov
\paper Fourier analysis in combinatorial number theory
\jour Russian Math. Surveys
\yr 2010
\vol 65
\issue 3
\pages 513--567
\mathnet{http://mi.mathnet.ru/eng/rm9355}
\crossref{https://doi.org/10.1070/RM2010v065n03ABEH004681}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2682721}
\zmath{https://zbmath.org/?q=an:05939727}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2010RuMaS..65..513S}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000281892100003}
\elib{https://elibrary.ru/item.asp?id=20425450}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-77958603320}
Linking options:
  • https://www.mathnet.ru/eng/rm9355
  • https://doi.org/10.1070/RM2010v065n03ABEH004681
  • https://www.mathnet.ru/eng/rm/v65/i3/p127
    • This publication is cited in the following 5 articles:
    1. Jincheng Zhuang, Qi Cheng, Jiejing Wen, “Solution counts and sums of roots of unity”, Journal of Number Theory, 240 (2022), 551  crossref
    2. 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
    3. Sanders T., “Bootstrapping Partition Regularity of Linear Systems”, Proc. Edinb. Math. Soc., 63:3 (2020), PII S0013091520000048, 630–653  crossref  mathscinet  isi  scopus
    4. Chapman J., Prendiville S., “On the Ramsey Number of the Brauer Configuration”, Bull. London Math. Soc., 52:2 (2020), 316–334  crossref  mathscinet  isi
    5. 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
    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:1877
    Russian version PDF:857
    English version PDF:89
    References:120
    First page:71
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025