{
  "id": "1612.04306",
  "version": "v1",
  "published": "2016-12-13T18:23:14.000Z",
  "updated": "2016-12-13T18:23:14.000Z",
  "title": "Higher Order Oscillating Sequences, Affine Distal Flows on the $d$-Torus, and Sarnak's Conjecture",
  "authors": [
    "Yunping Jiang"
  ],
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "In this paper, we give two precise definitions of a higher order oscillating sequence and show the importance of this concept in the study of Sarnak's conjecture. We prove that any higher order oscillating sequence of order $2$ is linearly disjoint from all affine distal flows on the $2$-torus. One consequence of this result is that any higher order oscillating sequence of order $2$ is linearly disjoint from all affine flows on the $2$-torus with zero topological entropy. In particular, this reconfirms Sarnak's conjecture for all affine flows on the $2$-torus with zero topological entropy. Furthermore, for $d>2$, we prove that any higher order oscillating sequence of order $d$ is linearly disjoint from all triangularizable affine distal flows on the $d$-torus. Thus it reconfirms Sarnak's conjecture for all triangularizable affine distal flows on the $d$-torus.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-13T18:23:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11K65",
      "37A35",
      "37A25",
      "11N05"
    ],
    "keywords": [
      "higher order oscillating sequence",
      "triangularizable affine distal flows",
      "reconfirms sarnaks conjecture",
      "zero topological entropy",
      "linearly disjoint"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}