{
  "id": "1507.01900",
  "version": "v1",
  "published": "2015-07-07T17:55:20.000Z",
  "updated": "2015-07-07T17:55:20.000Z",
  "title": "Energy integrals and small points for the Arakelov height",
  "authors": [
    "Paul Fili",
    "Clayton Petsche",
    "Igor Pritsker"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study small points for the Arakelov height on the projective line. First, we identify the smallest positive value taken by the Arakelov height, and we characterize all cases of equality. Next we solve several archimedean energy minimization problems with respect to the chordal metric on the projective line, and as an application, we obtain lower bounds on the Arakelov height in fields of totally real and totally p-adic numbers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-07T17:55:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G50",
      "11R06",
      "37P30"
    ],
    "keywords": [
      "arakelov height",
      "energy integrals",
      "archimedean energy minimization problems",
      "projective line",
      "smallest positive value taken"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150701900F"
    }
  }
}