{
  "id": "1801.02873",
  "version": "v1",
  "published": "2018-01-09T10:37:35.000Z",
  "updated": "2018-01-09T10:37:35.000Z",
  "title": "Vanishing of Hyperelliptic L-functions at the Central Point",
  "authors": [
    "Wanlin Li"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We obtain a lower bound on the number of quadratic Dirichlet L-functions over the rational function field which vanish at the central point $s = 1/2$. This is in contrast with the situation over the rational numbers, where a conjecture of Chowla predicts there should be no such L-functions. The approach is based on the observation that vanishing at the central point can be interpreted geometrically, as the existence of a map to a fixed abelian variety from the hyperelliptic curve associated to the character.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-09T10:37:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "central point",
      "hyperelliptic l-functions",
      "quadratic dirichlet l-functions",
      "rational function field",
      "lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}