{
  "id": "2210.03035",
  "version": "v1",
  "published": "2022-10-06T16:38:25.000Z",
  "updated": "2022-10-06T16:38:25.000Z",
  "title": "Quadratic enrichment of the logarithmic derivative of the zeta function",
  "authors": [
    "Margaret Bilu",
    "Wei Ho",
    "Padmavathi Srinivasan",
    "Isabel Vogt",
    "Kirsten Wickelgren"
  ],
  "comment": "38 pages",
  "categories": [
    "math.AG",
    "math.AT",
    "math.KT",
    "math.NT"
  ],
  "abstract": "We define an enrichment of the logarithmic derivative of the zeta function of a variety over a finite field to a power series with coefficients in the Grothendieck--Witt group. This enrichment is related to the topology of the real points of a lift. We show a rationality result for cellular schemes over a field, and compute several examples, including toric varieties.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-10-06T16:38:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "14G10",
      "14F42",
      "19D45",
      "55P25",
      "11G25"
    ],
    "keywords": [
      "zeta function",
      "logarithmic derivative",
      "quadratic enrichment",
      "cellular schemes",
      "rationality result"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}