{
  "id": "1005.4640",
  "version": "v2",
  "published": "2010-05-25T17:30:51.000Z",
  "updated": "2011-01-09T19:11:15.000Z",
  "title": "On the distribution of extreme values of zeta and $L$-functions in the strip $1/2<σ<1$",
  "authors": [
    "Youness Lamzouri"
  ],
  "comment": "45 pages. To appear in Int. Math. Res. Not",
  "categories": [
    "math.NT",
    "math.PR"
  ],
  "abstract": "We study the distribution of large (and small) values of several families of $L$-functions on a line $\\text{Re(s)}=\\sigma$ where $1/2<\\sigma<1$. We consider the Riemann zeta function $\\zeta(s)$ in the $t$-aspect, Dirichlet $L$-functions in the $q$-aspect, and $L$-functions attached to primitive holomorphic cusp forms of weight $2$ in the level aspect. For each family we show that the $L$-values can be very well modeled by an adequate random Euler product, uniformly in a wide range. We also prove new $\\Omega$-results for quadratic Dirichlet $L$-functions (predicted to be best possible by the probabilistic model) conditionally on GRH, and other results related to large moments of $\\zeta(\\sigma+it)$.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2011-01-09T19:11:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11F66",
      "60F10"
    ],
    "keywords": [
      "extreme values",
      "distribution",
      "adequate random euler product",
      "riemann zeta function",
      "primitive holomorphic cusp forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 45,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1005.4640L"
    }
  }
}