{
  "id": "2007.13265",
  "version": "v1",
  "published": "2020-07-27T01:22:50.000Z",
  "updated": "2020-07-27T01:22:50.000Z",
  "title": "Low-lying zeros of a family of quadratic Hecke $L$-functions via ratios conjecture",
  "authors": [
    "Peng Gao",
    "Liangyi Zhao"
  ],
  "comment": "15 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we apply the ratio conjecture of $L$-functions to derive the lower order terms of the $1$-level density of the low-lying zeros of a family quadratic Hecke $L$-functions in the Gaussian field. Up to the first lower order term, we show that our result is consistent with that obtained from previous work under the generalized Riemann hypothesis, when the Fourier transforms of the test functions are supported in $(-2, 2)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-07-27T01:22:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M26",
      "11M50"
    ],
    "keywords": [
      "low-lying zeros",
      "ratios conjecture",
      "first lower order term",
      "level density",
      "generalized riemann hypothesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}