{
  "id": "2312.12199",
  "version": "v1",
  "published": "2023-12-19T14:35:31.000Z",
  "updated": "2023-12-19T14:35:31.000Z",
  "title": "On derivatives of zeta and $L$-functions near the 1-line",
  "authors": [
    "Zikang Dong",
    "Yutong Song",
    "Weijia Wang",
    "Hao Zhang"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the conditional upper bounds and extreme values of derivatives of the Riemann zeta function and Dirichlet $L$-functions near the 1-line. Let $\\ell$ be a fixed natural number. We show that, if $|\\sigma-1|\\ll1/\\log_2t$, then $|\\zeta^{(\\ell)}(\\sigma+ i t)|$ has the same maximal order (up to the leading coefficients) as $|\\zeta^{(\\ell)}(1+ i t)|$ when $t\\to\\infty$. Similar results can be obtained for Dirichlet $L$-functions $L^{(\\ell)}(\\sigma,\\chi)$ with $\\chi\\pmod q$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-12-19T14:35:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "derivatives",
      "conditional upper bounds",
      "riemann zeta function",
      "fixed natural number",
      "extreme values"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}