{
  "id": "1405.0643",
  "version": "v1",
  "published": "2014-05-04T02:37:31.000Z",
  "updated": "2014-05-04T02:37:31.000Z",
  "title": "A note on the number of coefficients of automorphic $L-$functions for $GL_m$ with same signs",
  "authors": [
    "Chaohua Jia"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\pi$ be an irreducible unitary cuspidal representation of $GL_m({\\Bbb A}_{\\Bbb Q})$ and $L(s,\\,\\pi)$ be the global $L-$function attached to $\\pi$. If ${\\rm Re}(s)>1$, $L(s,\\,\\pi)$ has a Dirichlet series expression. When $\\pi$ is self-contragradient, all the coefficients of Dirichlet series are real. In this note, we shall give non-trivial lower bounds for the number of positive and negative coefficients respectively, which is an improvement on the recent work of Jianya Liu and Jie Wu.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-05-04T02:37:31.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "automorphic",
      "irreducible unitary cuspidal representation",
      "non-trivial lower bounds",
      "dirichlet series expression",
      "jianya liu"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1405.0643J"
    }
  }
}