{
  "id": "2410.09694",
  "version": "v1",
  "published": "2024-10-13T02:08:10.000Z",
  "updated": "2024-10-13T02:08:10.000Z",
  "title": "Matsuda monoids and Artin's primitive root conjecture",
  "authors": [
    "Sunil Naik"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-13T02:08:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A07",
      "11N56",
      "11N69",
      "11R45"
    ],
    "keywords": [
      "artins primitive root conjecture",
      "matsuda monoid",
      "christensen",
      "generalized riemann hypothesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}