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Mat. Sb., 2018, Volume 209, Number 4, Pages 117–142 (Mi msb8907)  

This article is cited in 2 scientific papers (total in 2 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

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.


DOI: https://doi.org/10.4213/sm8907

Full text: PDF file (734 kB)
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English version:
Sbornik: Mathematics, 2018, 209:4, 580–603

Bibliographic databases:

UDC: 511.218
MSC: 11B13, 11D04
Received: 05.01.2017 and 01.06.2017

Citation: I. D. Shkredov, “An application of the sum-product phenomenon to sets avoiding several linear equations”, Mat. Sb., 209:4 (2018), 117–142; Sb. Math., 209:4 (2018), 580–603

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm8907
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. S. V. Konyagin, I. D. Shkredov, “On subgraphs of random Cayley sum graphs”, European J. Combin., 70 (2018), 61–74  crossref  mathscinet  zmath  isi
    2. I. D. Shkredov, “A Short Remark on the Multiplicative Energy of the Spectrum”, Math. Notes, 105:3-4 (2019), 449–457  mathnet  crossref  crossref  mathscinet  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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