{
  "id": "1803.10982",
  "version": "v2",
  "published": "2018-03-29T09:36:16.000Z",
  "updated": "2018-07-25T06:50:45.000Z",
  "title": "Zeta Function at Zero for Surfaces with Boundary",
  "authors": [
    "Charles Hadfield"
  ],
  "comment": "17 pages, clarification of map defined in Section 4, minor change in proof of injectivity",
  "categories": [
    "math.DS"
  ],
  "abstract": "We study the Ruelle zeta function at zero for negatively curved oriented surfaces with boundary. At zero, the zeta function has a zero and its multiplicity is shown to be determined by the Euler characteristic of the surface. This is shown by considering certain Ruelle resonances and identifying their multiplicity with dimensions of the relative cohomology of the surface.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2018-07-25T06:50:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C30",
      "37D40",
      "58J50"
    ],
    "keywords": [
      "ruelle zeta function",
      "multiplicity",
      "euler characteristic",
      "ruelle resonances",
      "negatively curved oriented surfaces"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}