{
  "id": "1805.07990",
  "version": "v1",
  "published": "2018-05-21T11:24:38.000Z",
  "updated": "2018-05-21T11:24:38.000Z",
  "title": "Independence of Artin L-functions",
  "authors": [
    "Mircea Cimpoeas",
    "Florin Nicolae"
  ],
  "comment": "10 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K/\\mathbb Q$ be a finite Galois extension. Let $\\chi_1,\\ldots,\\chi_r$ be $r\\geq 1$ distinct characters of the Galois group with the associated Artin L-functions $L(s,\\chi_1),\\ldots, L(s,\\chi_r)$. Let $m\\geq 0$. We prove that the derivatives $L^{(k)}(s,\\chi_j)$, $1\\leq j\\leq r$, $0\\leq k\\leq m$, are linearly independent over the field of meromorphic functions of order $<1$. From this it follows that the L-functions corresponding to the irreducible characters are algebraically independent over the field of meromorphic functions of order $<1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-21T11:24:38.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11R42",
      "11M41"
    ],
    "keywords": [
      "independence",
      "meromorphic functions",
      "finite galois extension",
      "galois group",
      "distinct characters"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}