{
  "id": "1708.02671",
  "version": "v1",
  "published": "2017-08-08T22:46:02.000Z",
  "updated": "2017-08-08T22:46:02.000Z",
  "title": "Variants of the Riemann zeta function",
  "authors": [
    "Barry Brent"
  ],
  "comment": "23 pages, 12 figures",
  "categories": [
    "math.NT",
    "math.DS"
  ],
  "abstract": "We construct variants of the Riemann zeta function with convenient properties and make conjectures about their dynamics; some of the conjectures are based on an analogy with the dynamical system of zeta. More specifically, we study the family of functions $V_z: s \\mapsto \\zeta(s) \\exp (zs)$. We observe convergence of $V_z$ fixed points along nearly logarithmic spirals with initial points at zeta fixed points and centered upon Riemann zeros. We can approximate these spirals numerically, so they might afford a means to study the geometry of the relationship of zeta fixed points to Riemann zeros.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-08-08T22:46:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M26",
      "37F10",
      "30D05"
    ],
    "keywords": [
      "riemann zeta function",
      "zeta fixed points",
      "riemann zeros",
      "conjectures",
      "initial points"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}