Abstract
In this paper we examine Grosswald's conjecture on $g(p)$, the least primitive root modulo $p$. Assuming the Generalized Riemann Hypothesis (GRH), and building on previous work by Cohen, Oliveira e Silva and Trudgian, we resolve Grosswald's conjecture by showing that $g(p)< \sqrt{p} - 2$ for all $p>409$. Our method also shows that under GRH we have $\hat{g}(p)< \sqrt{p}-2$ for all $p>2791$, where $\hat{g}(p)$ is the least prime primitive root modulo $p$.
Citation
Kevin McGown. Enrique Treviño. Tim Trudgian. "Resolving Grosswald's conjecture on GRH." Funct. Approx. Comment. Math. 55 (2) 215 - 225, December 2016. https://doi.org/10.7169/facm/2016.55.2.5
Information