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Russian Mathematical Surveys, 2015, Volume 70, Issue 1, Pages 113–163
DOI: https://doi.org/10.1070/RM2015v070n01ABEH004938 (Mi rm9647) 		 
This article is cited in 1 scientific paper (total in 1 paper)

Structure theorems in additive combinatorics

I. D. Shkredovab

a Steklov Mathematical Institute of Russian Academy of Sciences
b Institute for Information Transmission Problems of the Russian Academy of Sciences (Kharkevich Institute)
English version PDF (952 kB) Citations (1)
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DOI: https://doi.org/10.1070/RM2015v070n01ABEH004938
Abstract: Several structure results of additive combinatorics are considered. Classical and modern problems of combinatorial number theory, higher-order Fourier analysis, inverse theorems for Gowers norms, higher energies, and the relationship between combinatorial and analytic number theory are discussed.
Bibliography: 149 titles.
Keywords: additive combinatorics, sets with the small doubling property, Gowers norms, Fourier analysis.
Funding agency Grant number
Russian Science Foundation 14-11-00433
This research was supported by the Russian Science Foundation (grant no. 14-11-00433).
Received: 27.08.2014
Russian version:
Uspekhi Matematicheskikh Nauk, 2015, Volume 70, Issue 1(421), Pages 123–178
DOI: https://doi.org/10.4213/rm9647
Bibliographic databases:
Document Type: Article
UDC: 511.34
MSC: Primary 11B30; Secondary 11B13, 11P70
Language: English
Original paper language: Russian
Citation: I. D. Shkredov, “Structure theorems in additive combinatorics”, Uspekhi Mat. Nauk, 70:1(421) (2015), 123–178; Russian Math. Surveys, 70:1 (2015), 113–163
Citation in format AMSBIB
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    • This publication is cited in the following 1 articles:
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    		Успехи математических наук Russian Mathematical Surveys
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    References:68
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