{
  "id": "2012.09091",
  "version": "v1",
  "published": "2020-12-16T17:19:39.000Z",
  "updated": "2020-12-16T17:19:39.000Z",
  "title": "Zero-free strips for the Riemann zeta-function derived from the Prime Number Theorem",
  "authors": [
    "Douglas Azevedo"
  ],
  "comment": "4 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We use the Prime Number Theorem to prove the existence of zero-free strips for the Riemann-zeta function. Precisely, we prove that there exists $\\delta>0$ for which if $0\\leq r<\\delta $ then $\\zeta(s)\\neq 0$ for Re$(s)>1-r$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-16T17:19:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M26",
      "11M41"
    ],
    "keywords": [
      "prime number theorem",
      "zero-free strips",
      "riemann zeta-function",
      "riemann-zeta function"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}