{
  "id": "1111.2236",
  "version": "v4",
  "published": "2011-11-09T15:23:40.000Z",
  "updated": "2012-04-17T12:41:06.000Z",
  "title": "Quadratic Residues and Non-residues in Arithmetic Progression",
  "authors": [
    "Steve Wright"
  ],
  "comment": "43 pages, 6 figures. Minor corrections and improvements to previous manuscript",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let S be an infinite set of non-empty, finite subsets of the nonnegative integers. If p is an odd prime, let c(p) denote the cardinality of the set {T {\\in} S : T {\\subseteq} {1,...,p-1} and T is a set of quadratic residues (respectively, non-residues) of p}. When S is constructed in various ways from the set of all arithmetic progressions of nonnegative integers, we determine the sharp asymptotic behavior of c(p) as p {\\to} +{\\infty}. Generalizations and variations of this are also established, and some problems connected with these results that are worthy of further study are discussed.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2012-04-17T12:41:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11D09",
      "11M99",
      "11L40"
    ],
    "keywords": [
      "arithmetic progression",
      "quadratic residues",
      "non-residues",
      "sharp asymptotic behavior",
      "nonnegative integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 43,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1111.2236W"
    }
  }
}