{
  "id": "1104.2542",
  "version": "v1",
  "published": "2011-04-13T16:35:43.000Z",
  "updated": "2011-04-13T16:35:43.000Z",
  "title": "The influence of the first term of an arithmetic progression",
  "authors": [
    "Daniel Fiorilli"
  ],
  "comment": "51 pages",
  "doi": "10.1112/plms/pds055",
  "categories": [
    "math.NT"
  ],
  "abstract": "The goal of this article is to study the discrepancy of the distribution of arithmetic sequences in arithmetic progressions. We will fix a sequence $\\A=\\{\\a(n)\\}_{n\\geq 1}$ of non-negative real numbers in a certain class of arithmetic sequences. For a fixed integer $a\\neq 0$, we will be interested in the behaviour of $\\A$ over the arithmetic progressions $a \\bmod q$, on average over $q$. Our main result is that for certain sequences of arithmetic interest, the value of $a$ has a significant influence on this distribution, even after removing the first term of the progressions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-04-13T16:35:43.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "arithmetic progression",
      "first term",
      "arithmetic sequences",
      "main result",
      "distribution"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 51,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1104.2542F"
    }
  }
}