{
  "id": "math/0609322",
  "version": "v2",
  "published": "2006-09-12T02:19:33.000Z",
  "updated": "2007-04-20T21:16:57.000Z",
  "title": "Approximating reals by sums of two rationals",
  "authors": [
    "Tsz Ho Chan"
  ],
  "comment": "13 pages, improved results and some changes in the proofs",
  "categories": [
    "math.NT"
  ],
  "abstract": "We generalize Dirichlet's diophantine approximation theorem to approximating any real number $\\alpha$ by a sum of two rational numbers $\\frac{a_1}{q_1} + \\frac{a_2}{q_2}$ with denominators $1 \\leq q_1, q_2 \\leq N$. This turns out to be related to the congruence equation problem $x y \\equiv c \\pmod q$ with $1 \\leq x, y \\leq q^{1/2 + \\epsilon}$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2007-04-20T21:16:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J04",
      "11A07",
      "11L40",
      "11L07"
    ],
    "keywords": [
      "approximating reals",
      "generalize dirichlets diophantine approximation theorem",
      "congruence equation problem",
      "real number",
      "rational numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......9322C"
    }
  }
}