{
  "id": "2105.02770",
  "version": "v1",
  "published": "2021-05-06T15:56:00.000Z",
  "updated": "2021-05-06T15:56:00.000Z",
  "title": "Functional equation of the $p$-adic $L$-function of Bianchi modular forms",
  "authors": [
    "Luis Santiago Palacios"
  ],
  "comment": "20 pages. Comments welcome!",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $K$ be an imaginary quadratic field with class number 1, in this paper we obtain the functional equation of the $p$-adic $L$-function of: (1) a small slope $p$-stabilisation of a Bianchi modular form, and (2) a critical slope $p$-stabilisation of a Base change Bianchi modular form that is $\\Sigma$-smooth. To treat case (2) we use $p$-adic families of Bianchi modular forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-05-06T15:56:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "functional equation",
      "base change bianchi modular form",
      "imaginary quadratic field",
      "treat case",
      "small slope"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}