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arXiv · 1401.2863

An explicit upper bound for the Helfgott delta in SL(2,p)

Jack Button·Colva Roney-Dougal
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Abstract

Helfgott proved that there exists a $\delta>0$ such that if $S$ is a symmetric generating subset of $SL(2,p)$ containing 1 then either $S^3=SL(2,p)$ or $|S^3|\geq |S|^{1+\delta}$. It is known that $\delta\geq 1/3024$. Here we show that $\delta\leq(\log_2(7)-1)/6 \approx 0.3012$ and we present evidence suggesting that this might be the true value of $\delta$.

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Jack Button, Colva Roney-Dougal. 2014-01-13. An explicit upper bound for the Helfgott delta in SL(2,p). https://arxiv.org/abs/1401.2863

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