Geodesic
Fourier analysis in combinatorial number theory
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 65 (2010) no. 3, pp. 513-567

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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. 
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     title = {Fourier analysis in combinatorial number theory},
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I. D. Shkredov. Fourier analysis in combinatorial number theory. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 65 (2010) no. 3, pp. 513-567. http://geodesic.mathdoc.fr/item/RM_2010_65_3_a3/