{
  "id": "2410.11193",
  "version": "v1",
  "published": "2024-10-15T02:16:59.000Z",
  "updated": "2024-10-15T02:16:59.000Z",
  "title": "Character sums, reciprocity and functional equations",
  "authors": [
    "Chung-Hang Kwan",
    "Wing Hong Leung"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this article, we examine the role of the recent banner of Spectral Reciprocity within the Langlands Beyond Endoscopy and Braverman-Kazhdan programmes. We present a novel four-variable character sum identity, which serves as a pivotal arithmetic input for the functional equations of automorphic L-functions. This identity can also be interpreted as a twisted, non-archimedean counterpart to Weber-type integrals from the theory of special functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-10-15T02:16:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F66",
      "11F72",
      "11L05",
      "11F12"
    ],
    "keywords": [
      "functional equations",
      "novel four-variable character sum identity",
      "pivotal arithmetic input",
      "spectral reciprocity",
      "special functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}