{
  "id": "1008.4970",
  "version": "v1",
  "published": "2010-08-29T23:04:37.000Z",
  "updated": "2010-08-29T23:04:37.000Z",
  "title": "Bounding $ζ(s)$ in the critical strip",
  "authors": [
    "Emanuel Carneiro",
    "Vorrapan Chandee"
  ],
  "journal": "Journal of Number Theory (Print), v. 131, p. 363-384, 2011",
  "doi": "10.1016/j.jnt.2010.08.002",
  "categories": [
    "math.NT"
  ],
  "abstract": "Assuming the Riemann Hypothesis, we make use of the recently discovered \\cite{CLV} extremal majorants and minorants of prescribed exponential type for the function $\\log\\left(\\tfrac{4 + x^2}{(\\alpha-1/2)^2 + x^2}\\right)$ to find upper and lower bounds with explicit constants for $\\log|\\zeta(\\alpha + it)|$ in the critical strip, extending the work of Chandee and Soundararajan \\cite{CS}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2010-08-29T23:04:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical strip",
      "riemann hypothesis",
      "extremal majorants",
      "prescribed exponential type",
      "lower bounds"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1008.4970C"
    }
  }
}