{
  "id": "1602.04317",
  "version": "v1",
  "published": "2016-02-13T11:20:26.000Z",
  "updated": "2016-02-13T11:20:26.000Z",
  "title": "On the regularity of primes in arithmetic progressions",
  "authors": [
    "Christian Elsholtz",
    "Niclas Technau",
    "Robert Tichy"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We prove that for a positive integer $k$ the primes in certain kinds of intervals can not distribute too 'uniformly' among the reduced residue classes modulo $k$. Hereby, we prove a generalization of a conjecture of Recaman and establish our results in a much more general situation, in particular for prime ideals in number fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-02-13T11:20:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arithmetic progressions",
      "regularity",
      "reduced residue classes modulo",
      "general situation",
      "prime ideals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}