{
  "id": "2103.00904",
  "version": "v1",
  "published": "2021-03-01T10:51:27.000Z",
  "updated": "2021-03-01T10:51:27.000Z",
  "title": "At least two of $ζ(5),ζ(7),\\ldots,ζ(35)$ are irrational",
  "authors": [
    "Li Lai",
    "Li Zhou"
  ],
  "comment": "13 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\zeta(s)$ be the Riemann zeta function. We prove the statement in the title, which improves a recent result of Rivoal and Zudilin by lowering $69$ to $35$. We also prove that at least one of $\\beta(2),\\beta(4),\\ldots,\\beta(10)$ is irrational, where $\\beta(s) = L(s,\\chi_4)$ and $\\chi_4$ is the Dirichlet character with conductor $4$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-01T10:51:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J72",
      "11M06",
      "33C20"
    ],
    "keywords": [
      "irrational",
      "riemann zeta function",
      "dirichlet character"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}