{
  "id": "math/9304211",
  "version": "v1",
  "published": "1993-04-01T00:00:00.000Z",
  "updated": "1993-04-01T00:00:00.000Z",
  "title": "On the distribution of sums of residues",
  "authors": [
    "Jerrold R. Griggs"
  ],
  "comment": "5 pages",
  "journal": "Bull. Amer. Math. Soc. (N.S.) 28 (1993) 329-333",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "We generalize and solve the $\\roman{mod}\\,q$ analogue of a problem of Littlewood and Offord, raised by Vaughan and Wooley, concerning the distribution of the $2^n$ sums of the form $\\sum_{i=1}^n\\varepsilon_ia_i$, where each $\\varepsilon_i$ is $0$ or $1$. For all $q$, $n$, $k$ we determine the maximum, over all reduced residues $a_i$ and all sets $P$ consisting of $k$ arbitrary residues, of the number of these sums that belong to $P$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1993-04-01T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "distribution",
      "arbitrary residues",
      "littlewood",
      "reduced residues"
    ],
    "tags": [
      "journal article",
      "expository article"
    ],
    "publication": {
      "publisher": "AMS",
      "journal": "Bull. Amer. Math. Soc."
    },
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1993math......4211G"
    }
  }
}