{
  "id": "math/0610119",
  "version": "v1",
  "published": "2006-10-03T15:47:59.000Z",
  "updated": "2006-10-03T15:47:59.000Z",
  "title": "A note on zeros of $L$-series of elliptic curves",
  "authors": [
    "Xian-Jin Li"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this note we study an analogy between a positive definite quadratic form for elliptic curves over finite fields and a positive definite quadratic form for elliptic curves over the rational number field. A question is posed of which an affirmative answer would imply the analogue of the Riemann hypothesis for elliptic curves over the rational number field.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-10-03T15:47:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M26"
    ],
    "keywords": [
      "elliptic curves",
      "positive definite quadratic form",
      "rational number field",
      "riemann hypothesis",
      "finite fields"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math.....10119L"
    }
  }
}