{
  "id": "1707.07183",
  "version": "v1",
  "published": "2017-07-22T16:06:00.000Z",
  "updated": "2017-07-22T16:06:00.000Z",
  "title": "Counting Multiplicities in a Hypersurface over a Number Field",
  "authors": [
    "Hao Wen"
  ],
  "comment": "15 pages",
  "categories": [
    "math.AG",
    "math.NT"
  ],
  "abstract": "We fix a counting function of multiplicities of rational points in a hypersurface of a projective space, and take the sum over all rational points of a bounded height. An upper bound for the sum with respect to this counting function will be given in terms of the degree of the hypersurface, the dimension of the singular locus and the upper bound of height. This upper bound gives a description of the complexity of the singular locus of this hypersurface.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-22T16:06:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "number field",
      "hypersurface",
      "counting multiplicities",
      "upper bound",
      "rational points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}