Abstract:
Using the theory of sum-products we prove that for an arbitrary κ⩽1/3 any subset of Fp avoiding t linear equations with three variables has size less than O(p/tκ).
Bibliography: 26 titles.
\Bibitem{Shk18}
\by I.~D.~Shkredov
\paper An application of the sum-product phenomenon to sets avoiding several linear equations
\jour Sb. Math.
\yr 2018
\vol 209
\issue 4
\pages 580--603
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Linking options:
https://www.mathnet.ru/eng/sm8907
https://doi.org/10.1070/SM8907
https://www.mathnet.ru/eng/sm/v209/i4/p117
This publication is cited in the following 4 articles:
A. Mohammadi, T. Pham, Y. Wang, “An energy decomposition theorem for matrices and related questions”, Can. Math. Bull., 66:4 (2023), 1280
I. D. Shkredov, Trigonometric Sums and Their Applications, 2020, 261
I. D. Shkredov, “A Short Remark on the Multiplicative Energy of the Spectrum”, Math. Notes, 105:3-4 (2019), 449–457
S. V. Konyagin, I. D. Shkredov, “On subgraphs of random Cayley sum graphs”, European J. Combin., 70 (2018), 61–74
Citation in format AMSBIB
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