{
  "id": "1807.00716",
  "version": "v1",
  "published": "2018-07-02T14:44:37.000Z",
  "updated": "2018-07-02T14:44:37.000Z",
  "title": "Voronoi summation for ${\\rm GL}_n$: collusion between level and modulus",
  "authors": [
    "Andrew Corbett"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We investigate the Voronoi summation problem for ${\\rm GL}_n$ in the level aspect for $n\\geq 2$. Of particular interest are those primes at which the level and modulus are jointly ramified - a common occurrence in analytic number theory when using techniques such as the Petersson trace formula. Building on previous legacies, our formula stands as the most general of its kind; in particular we extend the results of Ichino-Templier. We also give (classical) refinements of our formula and study the $p$-adic generalisations of the Hankel transform.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-07-02T14:44:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F30",
      "11S40"
    ],
    "keywords": [
      "petersson trace formula",
      "analytic number theory",
      "voronoi summation problem",
      "common occurrence",
      "level aspect"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}