Geodesic
An application of the sum-product phenomenon to sets avoiding several linear equations
Sbornik. Mathematics, Tome 209 (2018) no. 4, pp. 580-603

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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
Mots-clés : Fourier transform. 
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     author = {I. D. Shkredov},
     title = {An application of the sum-product phenomenon to sets avoiding several linear equations},
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I. D. Shkredov. An application of the sum-product phenomenon to sets avoiding several linear equations. Sbornik. Mathematics, Tome 209 (2018) no. 4, pp. 580-603. http://geodesic.mathdoc.fr/item/SM_2018_209_4_a5/