On the least primitive root of a prime
Let \(g(p)\) be the least positive primitive root of a prime \(p\). The authors prove that \(g(p)=O(m^c p^{1/2})\) where \(c\) is a constant and \(m\) is the number of distinct prime factors of \(p-1\). As \(m\) large, it is an improvement of a result of the reviewer: \(g(p)\leq 2^{m+1} p^{1/2}\). The authors introduce a lemma and then apply Brun's method to obtain the result. The lemma runs as following: Let \(S\) and \(T\) be two sets with distinct integers, mod \(p\). Then for any non-principal character \(\chi\), we have \[ \left|\sum_{u \in S, v \in T} \chi (u+v)\right|^2 \leq p \sum_{u \in S} 1 \sum_{v \in T} 1. \]
scientific article; zbMATH DE number 3129511