{
  "id": "2108.08171",
  "version": "v1",
  "published": "2021-08-18T14:25:48.000Z",
  "updated": "2021-08-18T14:25:48.000Z",
  "title": "Further insights into the mysteries of the values of zeta functions at integers",
  "authors": [
    "Ján Mináč",
    "Nguyen Duy Tân",
    "Nguyen Tho Tung"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We present a remarkably simple and surprisingly natural interpretation of the values of zeta functions at negative integers and zero. Namely we are able to relate these values to areas related to partial sums of powers. We apply these results to further interpretations of values of $L$-functions at negative integers. We hint in a very brief way at some expected connections of this work with other current efforts to understand the mysteries of the values of zeta functions at integers.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-18T14:25:48.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "zeta functions",
      "negative integers",
      "surprisingly natural interpretation",
      "current efforts",
      "partial sums"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}