{
  "id": "1701.06614",
  "version": "v1",
  "published": "2017-01-23T20:14:03.000Z",
  "updated": "2017-01-23T20:14:03.000Z",
  "title": "A congruence sum and rational approximations",
  "authors": [
    "Sandro Bettin"
  ],
  "comment": "7 pages, 2 figures, to appear in Rend. Circ. Mat. Palermo, II. Ser",
  "doi": "10.1007/s12215-016-0288-0",
  "categories": [
    "math.NT"
  ],
  "abstract": "We give a reciprocity formula for a two-variable sum where the variables satisfy a linear congruence condition. We also prove that such sum is a measure of how well a rational is approximable from below and show that the reciprocity formula is a simple consequence of this fact.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-01-23T20:14:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A55",
      "11A07",
      "11A15",
      "11N37",
      "11J70"
    ],
    "keywords": [
      "rational approximations",
      "congruence sum",
      "reciprocity formula",
      "linear congruence condition",
      "simple consequence"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Springer"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}