{
  "id": "math/9901051",
  "version": "v2",
  "published": "1999-01-12T22:00:49.000Z",
  "updated": "1999-02-01T16:00:04.000Z",
  "title": "Scattering on the p-adic field and a trace formula",
  "authors": [
    "Jean-Francois Burnol"
  ],
  "comment": "17 pages, plain TeX. v2 adds the evaluation of a trace considered by Connes",
  "journal": "Internat. Math. Res. Notices, 2000 No.2, pp57-70",
  "doi": "10.1155/S1073792800000040",
  "categories": [
    "math.NT"
  ],
  "abstract": "I apply the set-up of Lax-Phillips Scattering Theory to a non-archimedean local field. It is possible to choose the outgoing space and the incoming space to be Fourier transforms of each other. Key elements of the Lax-Phillips theory are seen to make sense and to have the expected interrelations: the scattering matrix S, the projection K to the interacting space, the contraction semi-group Z and the time delay operator T. The scattering matrix is causal, its analytic continuation has the expected poles and zeros, and its phase derivative is the (non-negative) spectral function of T, which is also the restriction to the diagonal of the kernel of K. The contraction semi-group Z is related to S (and T) through a trace formula. Introducing an odd-even grading on the interacting space allows to express the Weil local explicit formula in terms of a ``supertrace''. I also apply my methods to the evaluation of a trace considered by Connes.",
  "revisions": [
    {
      "version": "v2",
      "updated": "1999-02-01T16:00:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11R42"
    ],
    "keywords": [
      "trace formula",
      "p-adic field",
      "contraction semi-group",
      "weil local explicit formula",
      "time delay operator"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "Plain TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1999math......1051B"
    }
  }
}