{
  "id": "1507.04917",
  "version": "v1",
  "published": "2015-07-17T10:50:50.000Z",
  "updated": "2015-07-17T10:50:50.000Z",
  "title": "Finite Multiple zeta Values and Finite Euler Sums",
  "authors": [
    "Jianqiang Zhao"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "The alternating multiple harmonic sums are partial sums of the iterated infinite series defining the Euler sums which are the alternating version of the multiple zeta values. In this paper, we present some systematic structural results of the van Hamme type congruences of these sums, collected as finite Euler sums. Moreover, we relate this to the structure of the Euler sums which generalizes the corresponding result of the multiple zeta values. We also provide a few conjectures with extensive numerical support.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-17T10:50:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11A07",
      "11B68",
      "08A50"
    ],
    "keywords": [
      "finite multiple zeta values",
      "finite euler sums",
      "van hamme type congruences",
      "alternating multiple harmonic sums",
      "systematic structural results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150704917Z"
    }
  }
}