{
  "id": "1910.13586",
  "version": "v1",
  "published": "2019-10-30T00:02:50.000Z",
  "updated": "2019-10-30T00:02:50.000Z",
  "title": "An orthogonality relation for GL(4,R)",
  "authors": [
    "Dorian Goldfeld",
    "Eric Stade",
    "Michael Woodbury"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Orthogonality is a fundamental theme in representation theory and Fourier analysis. An orthogonality relation for characters of finite abelian groups (now recognized as an orthogonality relation on $\\mathrm{GL}(1)$) was used by Dirichlet to prove infinitely many primes in arithmetic progressions. Orthogonality relations for $\\mathrm{GL}(2)$ and $\\mathrm{GL}(3)$ have been worked on by many researchers with a broad range of applications to number theory. We present here, for the first time, very explicit orthogonality relations for the real group $\\mathrm{GL}(4,\\mathbb{R})$ with a power savings error term. The proof requires novel techniques in the computation of the geometric side of the Kuznetsov trace formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-30T00:02:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F55",
      "11F72"
    ],
    "keywords": [
      "power savings error term",
      "kuznetsov trace formula",
      "finite abelian groups",
      "explicit orthogonality relations",
      "geometric side"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}