{
  "id": "2407.20509",
  "version": "v1",
  "published": "2024-07-30T02:53:42.000Z",
  "updated": "2024-07-30T02:53:42.000Z",
  "title": "Interpolant of truncated multiple zeta functions",
  "authors": [
    "Kentaro Ihara",
    "Yayoi Nakamura",
    "Shuji Yamamoto"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We introduce an analytic function $\\Psi(s_1,\\ldots,s_r;w)$ that interpolates truncated multiple zeta functions $\\zeta_N(s_1,\\ldots,s_r)$. We represent this interpolant as a Mellin transform of a function $G(q_1,\\ldots,q_r;w)$ and, using this expression, give the analytic continuation. Further, the harmonic product relations for $\\Psi$ and $G$ are established via relevant Hopf algebra structures, and some properties of the function $G$ are provided.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-07-30T02:53:42.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "interpolant",
      "relevant hopf algebra structures",
      "interpolates truncated multiple zeta functions",
      "harmonic product relations",
      "analytic continuation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}