{
  "id": "1703.00261",
  "version": "v1",
  "published": "2017-03-01T12:22:26.000Z",
  "updated": "2017-03-01T12:22:26.000Z",
  "title": "A Variant of the Truncated Perron's Formula and Primitive Roots",
  "authors": [
    "D. S. Ramana",
    "O. Ramaré"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "We show under the Generalised Riemann Hypothesis that for every $\\delta>0$, almost every prime $q$ in $[Q,2Q]$ has the expected of prime primitive roots in the interval $[x,x+x^{\\frac{1}2+\\delta}]$ provided $Q$ is not more than $x^{\\frac{2}{3}-\\epsilon}$. We obtain this via a variant of the classical truncated Perron's formula for the partial sums of the coefficients of a Dirichlet series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-01T12:22:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11N05",
      "11M06"
    ],
    "keywords": [
      "dirichlet series",
      "prime primitive roots",
      "classical truncated perrons formula",
      "partial sums",
      "generalised riemann hypothesis"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}