{
  "id": "1209.0412",
  "version": "v1",
  "published": "2012-09-03T17:24:29.000Z",
  "updated": "2012-09-03T17:24:29.000Z",
  "title": "Discrete Subsets of Totally Imaginary Quartic Algebraic Integers in the Complex Plane",
  "authors": [
    "Wenhan Wang"
  ],
  "comment": "1 figure",
  "categories": [
    "math.NT"
  ],
  "abstract": "Algebraic integers in totally imaginary quartic number fields are not discrete in the complex plane under a fixed embedding, which makes it impossible to visualize all integers in the plane, unlike the quadratic imaginary algebraic integers. In this note we consider a naturally occurring discrete subset of the algebraic integers with similar properties as lattices. For the fifth cyclotomic field, we investigate those integers with absolute values under a fixed embedding in a given bound. We show that such integers form a discrete set in the complex plane. It is observed that this subset has quasi-periodic appearance. In particular, we also show that the distance between a fixed point to the most adjacent point in this subset takes only two possible values.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2012-09-03T17:24:29.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "totally imaginary quartic algebraic integers",
      "complex plane",
      "discrete subset",
      "imaginary quartic number fields",
      "quadratic imaginary algebraic integers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.0412W"
    }
  }
}