{
  "id": "1904.01714",
  "version": "v1",
  "published": "2019-04-03T00:20:30.000Z",
  "updated": "2019-04-03T00:20:30.000Z",
  "title": "A LeVeque-Type Inequality on the ring of $p$-adic integers",
  "authors": [
    "Naveen Somasunderam"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We derive an inequality on the discrepancy of sequences on the ring of $p$-adic integers $\\ZZ_p$ using techniques from Fourier analysis. The inequality is used to obtain an upper bound on the discrepancy of the sequence $\\alpha_n = na +b$, where $a$ and $b$ are elements of $\\ZZ_p$. This is a $p$-adic analogue of the classical LeVeque inequality on the circle group $\\RR/\\ZZ$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-04-03T00:20:30.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B99",
      "11K38",
      "11S82",
      "37P99",
      "43A75"
    ],
    "keywords": [
      "adic integers",
      "leveque-type inequality",
      "discrepancy",
      "circle group",
      "fourier analysis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}