{
  "id": "1402.4056",
  "version": "v1",
  "published": "2014-02-17T16:56:42.000Z",
  "updated": "2014-02-17T16:56:42.000Z",
  "title": "On twisted exterior and symmetric square $γ$-factors",
  "authors": [
    "Radhika Ganapathy",
    "Luis Lomelí"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We establish the existence and uniqueness of twisted exterior and symmetric square $\\gamma$-factors in positive characteristic by studying the Siegel Levi case of generalized spinor groups. The corresponding theory in characteristic zero is due to Shahidi. In addition, in characteristic $p$ we prove that these twisted local factors are compatible with the local Langlands correspondence. As a consequence, still in characteristic $p$, we obtain a proof of the stability property of $\\gamma$-factors under twists by highly ramified characters. Next we use the results on the compatibility of the Langlands-Shahidi local coefficients with the Deligne-Kazhdan theory over close local fields to show that the twisted symmetric and exterior square $\\gamma$-factors, $L$-functions and $\\varepsilon$-factors are preserved over close local fields. Furthermore, we obtain a formula for Plancherel measures in terms of local factors and we also show that they also preserved over close local fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-02-17T16:56:42.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F70",
      "11M38",
      "22E50",
      "22E55"
    ],
    "keywords": [
      "symmetric square",
      "close local fields",
      "twisted exterior",
      "langlands-shahidi local coefficients",
      "local langlands correspondence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1402.4056G"
    }
  }
}