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arXiv · 1811.07454

A note on conditional expanders over prime fields

Mozhgan Mirzaei
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Abstract

Let $\mathbb{F}_p$ be a prime field of order $p,$ and $A$ be a set in $\mathbb{F}_p$ with $|A| \leq p^{1/2}.$ In this note, we show that \[\max\{|A+A|, |f(A, A)|\}\gtrsim |A|^{\frac{6}{5}+\frac{4}{305}},\] where $f(x, y)$ is a non-degenerate quadratic polynomial in $\mathbb{F}_p[x, y].$ This improves a recent result given by Koh, Mojarrad, Pham, Valculescu (2018).

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Mozhgan Mirzaei. 2019-04-15. A note on conditional expanders over prime fields. https://arxiv.org/abs/1811.07454

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