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arXiv · 2410.09694

Matsuda monoids and Artin's primitive root conjecture

Sunil Naik
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Abstract

Let $M \subseteq \mathbb{N}_{0}$ be the additive submonoid generated by $2$ and $3$. In a recent work, Christensen, Gipson and Kulosman proved that $M$ is not a Matsuda monoid of type $2$ and type $3$ and they have raised the question of whether $M$ is a Matsuda monoid of type $\ell$ for any prime $\ell$. Assuming the generalized Riemann hypothesis, Daileda showed that $M$ is not a Matsuda monoid of type $\ell$ for any prime $\ell$. In this article, we will establish this result unconditionally using its' connection with Artin's primitive root conjecture and this resolves the question of Christensen, Gipson and Kulosman.

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Sunil Naik. 2024-10-13. Matsuda monoids and Artin's primitive root conjecture. https://arxiv.org/abs/2410.09694

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