{
  "id": "math/0503164",
  "version": "v2",
  "published": "2005-03-08T20:32:13.000Z",
  "updated": "2005-03-16T14:30:12.000Z",
  "title": "On a symmetric congruence and its applications",
  "authors": [
    "M. Z. Garaev",
    "A. A. Karatsuba"
  ],
  "comment": "19 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "For a large integer $m,$ we obtain an asymptotic formula for the number of solutions of a certain congruence modulo $m$ with four variables, where the variables belong to special sets of residue classes modulo $m.$ This formula are applied to obtain new information on the exceptional set of the multiplication table problem in a residue ring modulo $m$ and a new bound for a double trigonometric sum with an exponential function.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-03-16T14:30:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L07"
    ],
    "keywords": [
      "symmetric congruence",
      "applications",
      "residue classes modulo",
      "exponential function",
      "congruence modulo"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......3164G"
    }
  }
}