{
  "id": "math/0502507",
  "version": "v2",
  "published": "2005-02-24T05:38:15.000Z",
  "updated": "2005-03-14T16:53:07.000Z",
  "title": "Values of zeta functions at s=1/2",
  "authors": [
    "Niranjan Ramachandran"
  ],
  "comment": "Submitted version. IMRN (to appear)",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We study the behaviour near s=1/2 of zeta functions of varieties over finite fields F_q with q a square. The main result is an Euler-characteristic formula for the square of the special value at s=1/2. The Euler-characteristic is constructed from the Weil-etale cohomology of a certain supersingular elliptic curve.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2005-03-14T16:53:07.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "zeta functions",
      "supersingular elliptic curve",
      "weil-etale cohomology",
      "finite fields",
      "special value"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2005math......2507R"
    }
  }
}