{
  "id": "2212.07604",
  "version": "v1",
  "published": "2022-12-15T03:32:11.000Z",
  "updated": "2022-12-15T03:32:11.000Z",
  "title": "Solubility of Additive Forms of Twice Odd Degree over Totally Ramified Extensions of $\\mathbb{Q}_2$",
  "authors": [
    "Drew Duncan"
  ],
  "comment": "arXiv admin note: text overlap with arXiv:2207.09556",
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that an additive form of degree $d=2m$, $m$ odd over any totally ramified extension of $\\mathbb{Q}_2$ has a nontrivial zero if the number of variables $s$ satisifies $s \\ge \\frac{d^2}{4} + 3d + 1$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-15T03:32:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D72",
      "11D88",
      "11E76"
    ],
    "keywords": [
      "totally ramified extension",
      "twice odd degree",
      "additive form",
      "solubility"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}