{
  "id": "2408.15259",
  "version": "v1",
  "published": "2024-08-10T04:53:27.000Z",
  "updated": "2024-08-10T04:53:27.000Z",
  "title": "Mass Distribution for holomorphic cusp forms on the vertical geodesic",
  "authors": [
    "Qingfeng Sun",
    "Qizhi Zhang"
  ],
  "comment": "22 pages. arXiv admin note: substantial text overlap with arXiv:2111.04713 by other authors",
  "categories": [
    "math.NT"
  ],
  "abstract": "We compute the quantum variance of holomorphic cusp forms on the vertical geodesic for smooth compactly supported test functions. As an application we show that almost all holomorphic Hecke cusp forms, whose weights are in a short interval, satisfy QUE conjecture on the vertical geodesic.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-08-10T04:53:27.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "holomorphic cusp forms",
      "vertical geodesic",
      "mass distribution",
      "holomorphic hecke cusp forms",
      "smooth compactly supported test functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 22,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}