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arXiv · 1609.06489

An application of the sum-product phenomenon to sets having no solutions of several linear equations

Ilya D. Shkredov
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Abstract

We prove that for an arbitrary $\kappa \le \frac{1}{3}$ any subset of $\mathbf{F}_p$ avoiding $t$ linear equations with three variables has size less than $O(p/t^\kappa)$. We also find several applications to problems about so--called non--averaging sets, number of collinear triples and mixed energies.

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Ilya D. Shkredov. 2016-09-21. An application of the sum-product phenomenon to sets having no solutions of several linear equations. https://arxiv.org/abs/1609.06489

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