{
  "id": "1804.07936",
  "version": "v1",
  "published": "2018-04-21T10:27:58.000Z",
  "updated": "2018-04-21T10:27:58.000Z",
  "title": "The Lerch zeta function as a fractional derivative",
  "authors": [
    "Arran Fernandez"
  ],
  "comment": "10 pages; peer-reviewed and accepted in Banach Center Publications as part of proceedings of Number Theory Week 2017",
  "categories": [
    "math.CV",
    "math.CA",
    "math.NT"
  ],
  "abstract": "We derive and prove a new formulation of the Lerch zeta function as a fractional derivative of an elementary function. We demonstrate how this formulation interacts very naturally with basic known properties of Lerch zeta, and use the functional equation to obtain a second formulation in terms of fractional derivatives.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-21T10:27:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M35",
      "26A33"
    ],
    "keywords": [
      "lerch zeta function",
      "fractional derivative",
      "second formulation",
      "elementary function",
      "functional equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}