{
  "id": "1604.03224",
  "version": "v1",
  "published": "2016-04-12T02:58:40.000Z",
  "updated": "2016-04-12T02:58:40.000Z",
  "title": "One-Level density for holomorphic cusp forms of arbitrary level",
  "authors": [
    "Owen Barrett",
    "Paula Burkhardt",
    "Jonathan DeWitt",
    "Robert Dorward",
    "Steven J. Miller"
  ],
  "comment": "Version 1.0, 27 pages",
  "categories": [
    "math.NT",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In 2000 Iwaniec, Luo, and Sarnak proved for certain families of $L$-functions associated to holomorphic newforms of square-free level that, under the Generalized Riemann Hypothesis, as the conductors tend to infinity the one-level density of their zeros matches the one-level density of eigenvalues of large random matrices from certain classical compact groups in the appropriate scaling limit. We remove the square-free restriction by obtaining a trace formula for arbitrary level by using a basis developed by Blomer and Mili\\'cevi\\'c, which is of use for other problems as well.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-04-12T02:58:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M26",
      "11M41",
      "15A52"
    ],
    "keywords": [
      "holomorphic cusp forms",
      "one-level density",
      "arbitrary level",
      "large random matrices",
      "trace formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160403224B"
    }
  }
}