{
  "id": "1910.13669",
  "version": "v1",
  "published": "2019-10-30T04:54:05.000Z",
  "updated": "2019-10-30T04:54:05.000Z",
  "title": "An Investigation Into Several Explicit Burgess Inequalities",
  "authors": [
    "Forrest J. Francis"
  ],
  "comment": "16 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\chi$ be a Dirichlet character modulo $p$, a prime. In applications, one often needs estimates for short sums involving $\\chi$. One such estimate is the family of bounds known as Burgess' inequality. In this paper, we explore several small adjustments one can make to the work of Enrique Trevi\\~no on explicit versions of Burgess' inequality. These improvements can be used to show that, for $p > 10^{5}$, the least $k$th power non-residue modulo $p$ is no larger than $p^\\frac{1}{6}$. We also provide a quick improvement to the conductor bounds for norm-Euclidean cyclic fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-10-30T04:54:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L40"
    ],
    "keywords": [
      "inequality",
      "explicit burgess inequalities",
      "th power non-residue modulo",
      "investigation",
      "dirichlet character modulo"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}