{
  "id": "1908.03658",
  "version": "v1",
  "published": "2019-08-10T00:53:00.000Z",
  "updated": "2019-08-10T00:53:00.000Z",
  "title": "Discrete Measures and the Extended Riemann Hypothesis",
  "authors": [
    "Samuel Estala-Arias"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this work we show that the Riemann hypothesis for the Dedekind zeta--function $\\zeta_{\\mathrm{K}}(s)$ of an algebraic number field $\\mathrm{K}$ is equivalent to a problem of the rate of convergence of certain discrete measures defined arithmetically on the multiplicative group of positive real numbers to the measure $\\zeta_{\\mathrm{K}}(2)^{-1}\\kappa q dq $, where $\\kappa$ denotes the residue of $\\zeta_{\\mathrm{K}}(s)$ at $s=1$ and $dq$ the Lebesgue measure.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-08-10T00:53:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "extended riemann hypothesis",
      "discrete measures",
      "algebraic number field",
      "dedekind zeta-function",
      "positive real numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}