{
  "id": "1902.03217",
  "version": "v1",
  "published": "2019-02-08T18:27:53.000Z",
  "updated": "2019-02-08T18:27:53.000Z",
  "title": "A finiteness result for $p$-adic families of Bianchi modular forms",
  "authors": [
    "Vlad Serban"
  ],
  "comment": "20 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study $p$-adic families of cohomological automorphic forms for ${\\mathrm{GL}}(2)$ over imaginary quadratic fields and prove that families interpolating a Zariski-dense set of classical cuspidal automorphic forms only occur under very restrictive conditions. We show how to computationally determine when this is not the case and establish concrete examples of families interpolating only finitely many Bianchi modular forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-02-08T18:27:53.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "bianchi modular forms",
      "adic families",
      "finiteness result",
      "imaginary quadratic fields",
      "classical cuspidal automorphic forms"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}