I. D. Shkredov, “Examples of sets with large trigonometric sums”, Sb. Math., 198:12 (2007), 1805

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Sbornik: Mathematics, 2007, Volume 198, Issue 12, Pages 1805–1838
DOI: https://doi.org/10.1070/SM2007v198n12ABEH003907 (Mi sm3776)

This article is cited in 7 scientific papers (total in 7 papers)

Examples of sets with large trigonometric sums

I. D. Shkredov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

English version PDF (462 kB) Citations (7) Russian version article

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DOI: https://doi.org/10.1070/SM2007v198n12ABEH003907

Abstract: Let

A

$A$ be a subset of

$\mathbb Z/N\mathbb Z$ , and let

$R$ be a set of large Fourier coefficients of the set

$A$ . The question on the structure of

$R$ is related to inverse problems of additive number theory. Properties of

$R$ were studied by Chang, Green, and this author. The present paper is concerned with new results on sets of large Fourier coefficients. In addition, examples demonstrating the definitive character of earlier results are presented.
Bibliography: 27 titles.

Received: 11.10.2006 and 22.07.2007

Bibliographic databases:

UDC: 511.218+511.336

MSC: Primary 11L03; Secondary 42A05

Language: English

Original paper language: Russian

Citation: I. D. Shkredov, “Examples of sets with large trigonometric sums”, Sb. Math., 198:12 (2007), 1805–1838

Citation in format AMSBIB

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\vol 198

\issue 12

\pages 1805--1838

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Linking options:

https://www.mathnet.ru/eng/sm3776

https://doi.org/10.1070/SM2007v198n12ABEH003907

https://www.mathnet.ru/eng/sm/v198/i12/p105

This publication is cited in the following 7 articles:

I. D. Shkredov, “Structure theorems in additive combinatorics”, Russian Math. Surveys, 70:1 (2015), 113–163
T. Schoen, I. D. Shkredov, “Roth's theorem in many variables”, Israel J. Math., 199:1 (2014), 287–308
Sanders T., “On the Bogolyubov–Ruzsa lemma”, Anal. PDE, 5:3 (2012), 627–655
Sanders T., “On certain other sets of integers”, J. Anal. Math., 116 (2012), 53–82
Shkredov I.D., Yekhanin S., “Sets with large additive energy and symmetric sets”, J. Combin. Theory Ser A, 118:3 (2011), 1086–1093
I. D. Shkredov, “Fourier analysis in combinatorial number theory”, Russian Math. Surveys, 65:3 (2010), 513–567
Konyagin S.V., Shkredov I.D., “On one result of J. Bourgain”, Ukr. Math. J., 62:3 (2010), 380–419

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Statistics & downloads:
Abstract page:	597
Russian version PDF:	221
English version PDF:	18
References:	96
First page:	5

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