{
  "id": "2011.08732",
  "version": "v1",
  "published": "2020-11-17T16:10:11.000Z",
  "updated": "2020-11-17T16:10:11.000Z",
  "title": "On Artin's Conjecture: Pairs of Additive Forms",
  "authors": [
    "Miriam Sophie Kaesberg"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "It is established that for every pair of additive forms $f=\\sum_{i=1}^s a_i x_i^k, g=\\sum_{i=1}^s b_i x_i^k$ of degree $k$ in $s>2k^2$ variables the equations $f=g=0$ have a non-trivial $p$-adic solution for all odd primes $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-11-17T16:10:11.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D88",
      "11D72"
    ],
    "keywords": [
      "additive forms",
      "artins conjecture",
      "adic solution",
      "odd primes"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}