{
  "id": "0810.2292",
  "version": "v4",
  "published": "2008-10-13T19:49:35.000Z",
  "updated": "2010-02-03T21:48:20.000Z",
  "title": "Distribution of values of $L$-functions at the edge of the critical strip",
  "authors": [
    "Youness Lamzouri"
  ],
  "comment": "30 pages",
  "journal": "Proc. London Math. Soc. (3) 100 (2010) 835-863",
  "doi": "10.1112/plms/pdp050",
  "categories": [
    "math.NT",
    "math.PR"
  ],
  "abstract": "We prove several results on the distribution of values of $L$-functions at the edge of the critical strip, by constructing and studying a large class of random Euler products. Among new applications, we study families of symmetric power $L$-functions of holomorphic cusp forms in the level aspect (assuming the automorphy of these $L$-functions) at $s=1$, functions in the Selberg class (in the height aspect), and quadratic twists of a fixed $GL(m)/{\\Bbb Q}$-automorphic cusp form at $s=1$.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2010-02-03T21:48:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11N37"
    ],
    "keywords": [
      "critical strip",
      "distribution",
      "automorphic cusp form",
      "random euler products",
      "holomorphic cusp forms"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0810.2292L"
    }
  }
}