{
  "id": "2302.04049",
  "version": "v1",
  "published": "2023-02-08T13:40:24.000Z",
  "updated": "2023-02-08T13:40:24.000Z",
  "title": "On a Gross conjecture over imaginary quadratic fields",
  "authors": [
    "Saad El Boukhari"
  ],
  "comment": "17 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $k$ be an imaginary quadratic number field, and $F/k$ a finite abelian extension of Galois group $G$. We show that a Gross conjecture concerning the leading terms of Artin $L$-series holds for $F/k$ and all rational primes which are split in $k$ and which do not divide $6$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-02-08T13:40:24.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "imaginary quadratic fields",
      "imaginary quadratic number field",
      "finite abelian extension",
      "galois group",
      "series holds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}