{
  "id": "1304.2191",
  "version": "v2",
  "published": "2013-04-08T12:50:09.000Z",
  "updated": "2013-07-25T13:16:59.000Z",
  "title": "On the density of primes with a set of quadratic residues or non-residues in given arithmetic progression",
  "authors": [
    "Steve Wright"
  ],
  "comment": "26 pages, 1 figure. Several improvements to the previous version are made and several errors in that version are corrected. arXiv admin note: text overlap with arXiv:1111.2236",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\mathcal{A}$ denote a finite set of arithmetic progressions of positive integers and let $s \\geq 2$ be an integer. If the cardinality of $\\mathcal{A}$ is at least 2 and $U$ is the union formed by taking certain arithmetic progressions of length $s$ from each element of $\\mathcal{A}$, we calculate the asymptotic density of the set of all prime numbers $p$ such that $U$ is a set of quadratic residues (respectively, quadratic non-residues) of $p$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-07-25T13:16:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A15",
      "11M99"
    ],
    "keywords": [
      "arithmetic progression",
      "quadratic residues",
      "quadratic non-residues",
      "finite set",
      "prime numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1304.2191W"
    }
  }
}