{
  "id": "math/9912107",
  "version": "v1",
  "published": "1999-12-13T23:22:00.000Z",
  "updated": "1999-12-13T23:22:00.000Z",
  "title": "Mean values of L-functions and symmetry",
  "authors": [
    "J. Brian Conrey",
    "David W. Farmer"
  ],
  "comment": "23 pages, 6 figures",
  "categories": [
    "math.NT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "Recently Katz and Sarnak introduced the idea of a symmetry group attached to a family of L-functions, and they gave strong evidence that the symmetry group governs many properties of the distribution of zeros of the L-functions. We consider the mean-values of the L-functions and the mollified mean-square of the L-functions and find evidence that these are also governed by the symmetry group. We use recent work of Keating and Snaith to give a complete description of these mean values. We find a connection to the Barnes-Vign\\'eras $\\Gamma_2$-function and to a family of self-similar functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1999-12-13T23:22:00.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11F66",
      "81Q50"
    ],
    "keywords": [
      "mean values",
      "l-functions",
      "symmetry group governs",
      "gave strong evidence",
      "complete description"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math.....12107C"
    }
  }
}