{
  "id": "1405.5110",
  "version": "v1",
  "published": "2014-05-20T15:03:42.000Z",
  "updated": "2014-05-20T15:03:42.000Z",
  "title": "Low-lying zeros of elliptic curve L-functions: Beyond the ratios conjecture",
  "authors": [
    "Daniel Fiorilli",
    "James Parks",
    "Anders Södergren"
  ],
  "comment": "33 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the low-lying zeros of L-functions attached to quadratic twists of a given elliptic curve E defined over $\\mathbb Q$. We are primarily interested in the family of all twists coprime to the conductor of E and compute a very precise expression for the corresponding 1-level density. In particular, for test functions whose Fourier transforms have sufficiently restricted support, we are able to compute the 1-level density up to an error term that is significantly sharper than the square-root error term predicted by the L-functions Ratios Conjecture.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-20T15:03:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G40",
      "11M41",
      "11M50"
    ],
    "keywords": [
      "elliptic curve l-functions",
      "low-lying zeros",
      "l-functions ratios conjecture",
      "square-root error term",
      "precise expression"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.5110F"
    }
  }
}