{
  "id": "1905.02864",
  "version": "v1",
  "published": "2019-05-08T01:51:25.000Z",
  "updated": "2019-05-08T01:51:25.000Z",
  "title": "Möbius Disjointness for Nilsequences Along Short Intervals",
  "authors": [
    "Xiaoguang He",
    "Zhiren Wang"
  ],
  "comment": "35 pages",
  "categories": [
    "math.DS",
    "math.NT"
  ],
  "abstract": "For a nilmanifold $G/\\Gamma$, a $1$-Lipschitz continuous function $F$ and the M\\\"obius sequence $\\mu(n)$, we prove a bound on the decay of the averaged short interval correlation $$\\frac1{HN}\\sum_{n\\leq N}\\Big|\\sum_{h\\leq H} \\mu(n+h)F(g^{n+h}x)\\Big|$$ as $H,N\\to\\infty$. The bound is uniform in $g\\in G$, $x\\in G/\\Gamma$ and $F$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-08T01:51:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "möbius disjointness",
      "nilsequences",
      "averaged short interval correlation",
      "lipschitz continuous function",
      "nilmanifold"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}