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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

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English version:
Sbornik: Mathematics, 2018, 209:4, 580–603

Bibliographic databases:

Document Type: Article
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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    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, “Korotkoe zamechanie o multiplikativnoi energii spektra”, Matem. zametki, 105:3 (2019), 444–454  mathnet  crossref  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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