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Sbornik: Mathematics, 2018, Volume 209, Issue 4, Pages 580–603
DOI: https://doi.org/10.1070/SM8907 (Mi sm8907) 		 
This article is cited in 4 scientific papers (total in 4 papers)

An application of the sum-product phenomenon to sets avoiding several linear equations

I. D. Shkredov

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
English version PDF (585 kB) Citations (4) Russian version article
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DOI: https://doi.org/10.1070/SM8907
Abstract: Using the theory of sum-products we prove that for an arbitrary $\kappa \le 1/3$ any subset of $\mathbb{F}_p$ avoiding $t$ linear equations with three variables has size less than $O(p/t^\kappa)$.
Bibliography: 26 titles.
Keywords: additive combinatorics, sum-product, Fourier transform.
Funding agency Grant number
Russian Science Foundation 14-11-00433
This work was supported by the Russian Science Foundation under grant no. 14-11-00433.
Received: 05.01.2017 and 01.06.2017
Bibliographic databases:
Document Type: Article
UDC: 511.218
MSC: 11B13, 11D04
Language: English
Original paper language: Russian
Citation: I. D. Shkredov, “An application of the sum-product phenomenon to sets avoiding several linear equations”, Sb. Math., 209:4 (2018), 580–603
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/sm/v209/i4/p117
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математический сборник Sbornik: Mathematics
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    Abstract page:566
    Russian version PDF:44
    English version PDF:10
    References:52
    First page:39
     
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