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

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 $|S^3|\ge |S{|}^{1+\delta }$. It is known that $\delta \ge 1/3024$. Here we show that $\delta \le ({\log }_2(7)-1)/6\approx 0.3012$ and we present evidence suggesting that this might be the true value of $\delta$.

arXiv comment20 pages, 0 figures, accepted version