{
  "id": "2409.06546",
  "version": "v1",
  "published": "2024-09-10T14:21:10.000Z",
  "updated": "2024-09-10T14:21:10.000Z",
  "title": "A family of integrals related to values of the Riemann zeta function",
  "authors": [
    "Rahul Kumar",
    "Paul Levrie",
    "Jean-Christophe Pain",
    "Victor Scharaschkin"
  ],
  "comment": "submitted to \"International Journal of Number Theory\"",
  "categories": [
    "math.NT"
  ],
  "abstract": "We propose a relation between values of the Riemann zeta function $\\zeta$ and a family of integrals. This results in an integral representation for $\\zeta(2p)$, where $p$ is a positive integer, and an expression of $\\zeta(2p+1)$ involving one of the above mentioned integrals together with a harmonic-number sum. Simplification of the latter eventually leads to an integral representation of $\\zeta(2p + 1)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-09-10T14:21:10.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann zeta function",
      "integral representation",
      "harmonic-number sum",
      "expression",
      "positive integer"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}