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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
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.
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”, Sb. Math., 209:4 (2018), 580–603
Linking options:
https://www.mathnet.ru/eng/sm8907https://doi.org/10.1070/SM8907 https://www.mathnet.ru/eng/sm/v209/i4/p117
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Abstract page: | 567 | Russian version PDF: | 45 | English version PDF: | 10 | References: | 52 | First page: | 39 |
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