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arXiv · 1508.05182

Resolving Grosswald's conjecture on GRH

Kevin McGown·Enrique Treviño·Tim Trudgian
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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 $p$.

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Kevin McGown, Enrique Treviño, Tim Trudgian. 2015-08-21. Resolving Grosswald's conjecture on GRH. https://arxiv.org/abs/1508.05182

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