{
  "id": "2101.06163",
  "version": "v1",
  "published": "2021-01-15T15:14:29.000Z",
  "updated": "2021-01-15T15:14:29.000Z",
  "title": "An elementary proof for a generalization of a Pohst's inequality",
  "authors": [
    "Francesco Battistoni",
    "Giuseppe Molteni"
  ],
  "comment": "9 pages",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let $P_n(y_1,\\ldots,y_n):= \\prod_{1\\leq i<j\\leq n}\\left( 1 -\\frac{y_i}{y_j}\\right) $ and $P_n:= \\sup_{(y_1,\\ldots,y_n)}P_n(y_1,\\ldots,y_n) $ where the supremum is taken over the $n$-ples $(y_1,\\ldots,y_n)$ of real numbers satisfying $0 <|y_1| < |y_2|< \\cdots < |y_n|$. We prove that $P_n \\leq 2^{\\lfloor n/2\\rfloor}$ for every $n$, i.e., we extend to all $n$ the bound that Pohst proved for $n\\leq 11$. As a consequence, the bound for the absolute discriminant of a totally real field in terms of its regulator is now proved for every degree of the field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-01-15T15:14:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "elementary proof",
      "pohsts inequality",
      "generalization",
      "absolute discriminant",
      "totally real field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}