{
  "id": "2012.00542",
  "version": "v1",
  "published": "2020-12-01T14:56:21.000Z",
  "updated": "2020-12-01T14:56:21.000Z",
  "title": "On the Northcott property for special values of L-functions",
  "authors": [
    "Fabien Pazuki",
    "Riccardo Pengo"
  ],
  "comment": "28 pages. Comments are very welcome!",
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We propose an investigation on the Northcott, Bogomolov and Lehmer properties for special values of $L$-functions. We first introduce an axiomatic approach to these three properties. We then focus on the Northcott property for special values of $L$-functions. We prove that such a property holds for the special value at zero of Dedekind zeta functions of number fields. In the case of $L$-functions of pure motives, we prove a Northcott property for special values located at the left of the critical strip, assuming the validity of the functional equation.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-01T14:56:21.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11G40",
      "11G50",
      "14K05",
      "11F67"
    ],
    "keywords": [
      "special value",
      "northcott property",
      "l-functions",
      "dedekind zeta functions",
      "axiomatic approach"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}