{
  "id": "0801.3176",
  "version": "v3",
  "published": "2008-01-21T11:56:43.000Z",
  "updated": "2008-11-03T17:08:04.000Z",
  "title": "Explicit calculations of automorphic forms for definite unitary groups",
  "authors": [
    "David Loeffler"
  ],
  "comment": "This version fixes an error pointed out by my PhD examiners -- the previous version cited a form of Ramanujan's conjecture which is in fact false. Accompanying computer programs available from http://www.ma.ic.ac.uk/~dl505/",
  "journal": "LMS J. Comput. Math 11 (2008), 326-342",
  "doi": "10.1112/S1461157000000620",
  "categories": [
    "math.NT"
  ],
  "abstract": "I give an algorithm for computing the full space of automorphic forms for definite unitary groups over Q, and apply this to calculate the automorphic forms of level $G(Z-hat)$ and various small weights for an example of a rank 3 unitary group. This leads to some examples of various types of endoscopic lifting from automorphic forms for U_1 x U_1 x U_1 and U_1 x U_2, and to an example of a non-endoscopic form of weight (3,3) corresponding to a family of 3-dimensional irreducible l-adic Galois representations. I also compute the 2-adic slopes of some automorphic forms with level structure at 2, giving evidence for the local constancy of the slopes.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-11-03T17:08:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F55"
    ],
    "keywords": [
      "automorphic forms",
      "definite unitary groups",
      "explicit calculations",
      "irreducible l-adic galois representations",
      "non-endoscopic form"
    ],
    "tags": [
      "dissertation",
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0801.3176L"
    }
  }
}