{
  "id": "1811.04915",
  "version": "v1",
  "published": "2018-11-12T18:53:04.000Z",
  "updated": "2018-11-12T18:53:04.000Z",
  "title": "Weyl Asymptotics for Perturbations of Morse Potential and Connections to the Riemann Zeta Function",
  "authors": [
    "Rob Rahm"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Let $N(T;V)$ denote the number of eigenvalues of the Schr\\\"odinger operator $-y'' + Vy$ with absolute value less than $T$. This paper studies the Weyl asymptotics of perturbations of the Schr\\\"odinger operator $-y'' + \\frac{1}{4}e^{2t}y$ on $[x_0,\\infty)$. In particular, we show that perturbations by functions $\\varepsilon(t)$ that satisfy $\\left|\\varepsilon(t)\\right|\\lesssim e^{t}$ do not change the Weyl asymptotics very much. Special emphasis is placed on connections to the asymptotics of the zeros of the Riemann zeta function.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-11-12T18:53:04.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "32L40",
      "34B24",
      "11M26"
    ],
    "keywords": [
      "riemann zeta function",
      "weyl asymptotics",
      "morse potential",
      "perturbations",
      "connections"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}