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Izvestiya: Mathematics, 2008, Volume 72, Issue 1, Pages 149–168
DOI: https://doi.org/10.1070/IM2008v072n01ABEH002396 (Mi im1140) 		 
This article is cited in 20 scientific papers (total in 20 papers)

On sets of large trigonometric sums

I. D. Shkredov

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
English version PDF (336 kB) Citations (20)
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DOI: https://doi.org/10.1070/IM2008v072n01ABEH002396
Abstract: We prove the existence of non-trivial solutions of the equation $r_1+r_2=r_3+r_4$, where $r_1$, $r_2$, $r_3$ and $r_4$ belong to the set $R$ of large Fourier coefficients of a certain subset $A$ of $\mathbb Z/N\mathbb Z$. This implies that $R$ has strong additive properties. We discuss generalizations and applications of the results obtained.
Received: 12.07.2006
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2008, Volume 72, Issue 1, Pages 161–182
DOI: https://doi.org/10.4213/im1140
Bibliographic databases:
UDC: 511.218+511.336
MSC: 11B25, 05D10, 11L07, 37C25, 37B20, 37A05, 28D05
Language: English
Original paper language: Russian
Citation: I. D. Shkredov, “On sets of large trigonometric sums”, Izv. RAN. Ser. Mat., 72:1 (2008), 161–182; Izv. Math., 72:1 (2008), 149–168
Citation in format AMSBIB
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    • This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:722
    Russian version PDF:258
    English version PDF:22
    References:80
    First page:3
     
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