{
  "id": "1801.00838",
  "version": "v1",
  "published": "2018-01-02T21:17:12.000Z",
  "updated": "2018-01-02T21:17:12.000Z",
  "title": "Differential equations in automorphic forms",
  "authors": [
    "Kim Klinger-Logan"
  ],
  "comment": "32 pages",
  "categories": [
    "math.NT",
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "Physicists such as Green, Vanhove, et al show that differential equations involving automorphic forms govern the behavior of gravitons. One particular point of interest is solutions to $(\\Delta-\\lambda)u=E_{\\alpha} E_{\\beta}$ on an arithmetic quotient of the exceptional group $E_8$. We use spectral theory solve $(\\Delta-\\lambda)u=E_{\\alpha}E_{\\beta}$ on the simpler space $SL_2(\\mathbb{Z})\\backslash SL_2(\\mathbb{R})$. The construction of such a solution uses Arthur truncation, the Maass-Selberg formula, and automorphic Sobolev spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-02T21:17:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automorphic forms",
      "differential equations",
      "automorphic sobolev spaces",
      "maass-selberg formula",
      "arthur truncation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}