{
  "id": "2206.09234",
  "version": "v1",
  "published": "2022-06-18T16:19:13.000Z",
  "updated": "2022-06-18T16:19:13.000Z",
  "title": "Analytic continuation of the Lerch zeta function",
  "authors": [
    "Rintaro Kozuma"
  ],
  "categories": [
    "math.CV",
    "math.NT"
  ],
  "abstract": "We give two results on the Lerch zeta function $\\Phi(z,\\,s,\\,w)$. The first is to give an explicitly brief proof providing both the analytic continuation of $\\Phi$ in $n$-variables $(n \\in \\{1,\\,2,\\,3\\})$ to maximal domains of holomorphy in $\\mathbb{C}^n$ and an extended formula for the special values of $\\Phi$ at non-positive integers in the variable $s$. The second is to show that Lerch's functional equation is essentially the same as Apostol's functional equation using the first result.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-06-18T16:19:13.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "lerch zeta function",
      "analytic continuation",
      "apostols functional equation",
      "lerchs functional equation",
      "maximal domains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}