{
  "id": "1906.08741",
  "version": "v1",
  "published": "2019-06-20T16:36:53.000Z",
  "updated": "2019-06-20T16:36:53.000Z",
  "title": "Two supercongruences related to multiple harmonic sums",
  "authors": [
    "Roberto Tauraso"
  ],
  "comment": "This is a preliminary version. Comments are welcome",
  "categories": [
    "math.NT",
    "math.CO"
  ],
  "abstract": "Let $p$ be a prime and let $x$ be a $p$-adic integer. We provide two supercongruences for truncated series of the form $$\\sum_{k=1}^{p-1} \\frac{(x)_k}{(1)_k}\\cdot \\frac{1}{k}\\sum_{1\\le j_1\\le\\cdots\\le j_r\\le k}\\frac{1}{j_1^{}\\cdots j_r^{}}\\quad\\mbox{and}\\quad \\sum_{k=1}^{p-1} \\frac{(x)_k(1-x)_k}{(1)_k^2}\\cdot \\frac{1}{k}\\sum_{1\\le j_1\\le\\cdots\\le j_r\\le k}\\frac{1}{j_1^{2}\\cdots j_r^{2}}.$$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-06-20T16:36:53.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A07",
      "11B65",
      "11B68"
    ],
    "keywords": [
      "multiple harmonic sums",
      "supercongruences",
      "adic integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}