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Uspekhi Mat. Nauk, 2015, Volume 70, Issue 1(421), Pages 123–178 (Mi umn9647)  

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)

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).


DOI: https://doi.org/10.4213/rm9647

Full text: PDF file (1031 kB)
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English version:
Russian Mathematical Surveys, 2015, 70:1, 113–163

Bibliographic databases:

Document Type: Article
UDC: 511.34
MSC: Primary 11B30; Secondary 11B13, 11P70
Received: 27.08.2014

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

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