{
  "id": "math/0408293",
  "version": "v1",
  "published": "2004-08-22T07:24:54.000Z",
  "updated": "2004-08-22T07:24:54.000Z",
  "title": "Epsilon factor for GL_l \\times GL_{l'}; l\\neq l' primes",
  "authors": [
    "Tetsuya Takahashi"
  ],
  "comment": "14 pages",
  "categories": [
    "math.NT",
    "math.RT"
  ],
  "abstract": "Let $F$ be a non-Archimedean local field with finite residual field of characteristic $p$. In this article we calculate the $\\epsilon$-factor of pairs for $\\GL_l(F) \\times \\GL_{l'}(F)$ where $l$ and $l'$ are distinct primes including the case $l=p$. For this calculation, we use the local Langlands correspondence and non-Galois base change lift. This method leads to the explicit conjecture of the $\\epsilon$-factor of the representations of $\\GL_m \\times \\GL_n$ when $n$ is relatively prime to $m$ and $p$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-08-22T07:24:54.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "22E50",
      "11F70"
    ],
    "keywords": [
      "epsilon factor",
      "non-galois base change lift",
      "non-archimedean local field",
      "finite residual field",
      "local langlands correspondence"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 14,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......8293T"
    }
  }
}