{
  "id": "2408.14524",
  "version": "v1",
  "published": "2024-08-26T09:31:04.000Z",
  "updated": "2024-08-26T09:31:04.000Z",
  "title": "On characterization of prime divisors of the index of a quadrinomial",
  "authors": [
    "Tapas Chatterjee",
    "Karishan Kumar"
  ],
  "comment": "23 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\theta$ be an algebraic integer and $f(x)=x^{n}+ax^{n-1}+bx+c$ be the minimal polynomial of $\\theta$ over the rationals. Let $K=\\mathbb{Q}(\\theta)$ be a number field and $\\mathcal{O}_{K}$ be the ring of integers of $K.$ In this article, we characterize all the prime divisors of the discriminant of $f(x)$ which do not divide the index of $f(x).$ As a fascinating corollary, we deduce necessary and sufficient conditions for the monogenity of the field $K=\\mathbb{Q}(\\theta),$ where $\\theta$ is associated with certain quadrinomials.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-26T09:31:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R04",
      "11R29",
      "11Y40",
      "11R09",
      "11R21"
    ],
    "keywords": [
      "prime divisors",
      "quadrinomial",
      "characterization",
      "sufficient conditions",
      "algebraic integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}