{
  "id": "1711.08928",
  "version": "v1",
  "published": "2017-11-24T11:20:11.000Z",
  "updated": "2017-11-24T11:20:11.000Z",
  "title": "The $a$-values of the Riemann zeta function near the critical line",
  "authors": [
    "Junsoo Ha",
    "Yoonbok Lee"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the value distribution of the Riemann zeta function near the line $\\Re s = 1/2$. We find an asymptotic formula for the number of $a$-values in the rectangle $ 1/2 + h_1 / (\\log T)^\\theta \\leq \\Re s \\leq 1/2+ h_2 /(\\log T)^\\theta $, $T \\leq \\Im s \\leq 2T$ for fixed $h_1, h_2>0$ and $ 0 < \\theta <1/13$. To prove it, we need an extension of the valid range of Lamzouri, Lester and Radziwi\\l\\l's recent results on the discrepancy between the distribution of $\\zeta(s)$ and its random model. We also propose the secondary main term for the Selberg's central limit theorem by providing sharper estimates on the line $\\Re s = 1/2 + 1/(\\log T)^\\theta $.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-11-24T11:20:11.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "riemann zeta function",
      "critical line",
      "selbergs central limit theorem",
      "secondary main term",
      "sharper estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}