{
  "id": "1805.07163",
  "version": "v1",
  "published": "2018-05-18T12:12:25.000Z",
  "updated": "2018-05-18T12:12:25.000Z",
  "title": "The maximum size of short character sums",
  "authors": [
    "Marc Munsch"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In the present note, we prove new lower bounds on large values of character sums $\\Delta(x,q):=\\max_{\\chi \\neq \\chi_0} \\vert \\sum_{n\\leq x} \\chi(n)\\vert$ in certain ranges of $x$. Employing an implementation of the resonance method developed in a work involving the author in order to exhibit large values of $L$- functions, we improve some results of Hough in the range $\\log x = o(\\sqrt{\\log q})$. Our results are expressed using the counting function of $y$- friable integers less than $x$ where we improve the level of smoothness $y$ for short intervals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-18T12:12:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L40",
      "11N25"
    ],
    "keywords": [
      "short character sums",
      "maximum size",
      "large values",
      "short intervals",
      "lower bounds"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}