{
  "id": "2001.03265",
  "version": "v1",
  "published": "2020-01-10T00:53:15.000Z",
  "updated": "2020-01-10T00:53:15.000Z",
  "title": "Type-I contributions to the one and two level densities of quadratic Dirichlet $L$--functions over function fields",
  "authors": [
    "Hung M. Bui",
    "Alexandra Florea",
    "Jonathan Keating"
  ],
  "comment": "23 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Using the Ratios Conjecture, we write down precise formulas with lower order terms for the one and the two level densities of zeros of quadratic Dirichlet $L$--functions over function fields. We denote the various terms arising as Type-$0$, Type-I and Type-II contributions. When the support of the Fourier transform of the test function is sufficiently restricted, we rigorously compute the Type-$0$ and Type-I terms and confirm that they match the conjectured answer. When the restrictions on the support are relaxed, our results suggest that Type-II contributions become important in the two level density.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-01-10T00:53:15.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "level density",
      "quadratic dirichlet",
      "function fields",
      "type-i contributions",
      "type-ii contributions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}