{
  "id": "1703.08344",
  "version": "v1",
  "published": "2017-03-24T10:30:57.000Z",
  "updated": "2017-03-24T10:30:57.000Z",
  "title": "On the coefficients of symmetric power $L$-functions",
  "authors": [
    "Jaban Meher",
    "Karam Deo Shankhadhar",
    "G. K. Viswanadham"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We study the signs of the Fourier coefficients of a newform. Let $f$ be a normalized newform of weight $k$ for $\\Gamma_0(N)$. Let $a_f(n)$ be the $n$th Fourier coefficient of $f$. For any fixed positive integer $m$, we study the distribution of the signs of $\\{a_f(p^m)\\}_p$, where $p$ runs over all prime numbers. We also find out the abscissas of absolute convergence of two Dirichlet series with coefficients involving the Fourier coefficients of cusp forms and the coefficients of symmetric power $L$-functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-24T10:30:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "symmetric power",
      "th fourier coefficient",
      "prime numbers",
      "absolute convergence",
      "dirichlet series"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}