{
  "id": "2401.12775",
  "version": "v1",
  "published": "2024-01-23T14:01:27.000Z",
  "updated": "2024-01-23T14:01:27.000Z",
  "title": "On $p$-adic Hurwitz-type spectral zeta functions",
  "authors": [
    "Su Hu",
    "Min-Soo Kim"
  ],
  "comment": "19 pages",
  "categories": [
    "math.NT",
    "math-ph",
    "math.CA",
    "math.MP"
  ],
  "abstract": "Let $\\left\\{E_n\\right\\}_{n=1}^{\\infty}$ be the set of energy levels corresponding to a Hamiltonian $H$. Denote by $$\\lambda_{0}=0~~\\textrm{and}~~\\lambda_{n}=E_{n}$$ for $n\\in\\mathbb N.$ In this paper, we shall construct and investigate the $p$-adic counterparts of the Hurwitz-type spectral zeta function \\begin{equation} \\zeta^{H}(s,\\lambda)=\\sum_{n=0}^{\\infty}\\frac{1}{(\\lambda_{n}+\\lambda)^{s}} \\end{equation} and its alternating form \\begin{equation} \\zeta_{E}^{H}(s,\\lambda)=2\\sum_{n=0}^{\\infty}\\frac{(-1)^{n}}{(\\lambda_{n}+\\lambda)^{s}} \\end{equation} in a parallel way.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-01-23T14:01:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M35",
      "11S80",
      "11B68",
      "81Q10"
    ],
    "keywords": [
      "adic hurwitz-type spectral zeta functions",
      "adic counterparts",
      "parallel way",
      "energy levels corresponding"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}