{
  "id": "2108.12935",
  "version": "v1",
  "published": "2021-08-29T23:36:39.000Z",
  "updated": "2021-08-29T23:36:39.000Z",
  "title": "Explicit asymptotic expansions in p-adic harmonic analysis II",
  "authors": [
    "Loren Spice"
  ],
  "comment": "74 pages",
  "categories": [
    "math.RT"
  ],
  "abstract": "We unwind the induction implicit in the \"one-step\" asymptotic expansions of arXiv:1701.02417 to describe how to turn asymptotic expansions, such as (but not limited to) the Harish-Chandra--Howe local character expansion, for depth-(0) supercuspidal characters into Kim--Murnaghan-type asymptotic expansions for arbitrary positive-depth, tame, supercuspidal characters. Doing so requires analogous results for Fourier transforms of orbital integrals on the Lie algebra of a reductive group, which are of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-29T23:36:39.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "22E35"
    ],
    "keywords": [
      "p-adic harmonic analysis",
      "explicit asymptotic expansions",
      "harish-chandra-howe local character expansion",
      "supercuspidal characters",
      "kim-murnaghan-type asymptotic expansions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 74,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}