{
  "annotation_id": "6a311c60-ba46-49d4-a89d-c6fd66f59692",
  "date_created": "2026-02-17T05:53:24.342000Z",
  "date_modified": "2026-02-17T05:53:24.342000Z",
  "file_hash": "a6513ce9d23abd0386617dbc0038632e3910f043b3213bc0ade1bcb2adef0581",
  "private": false,
  "record": {
    "abstract": "In this paper, we establish analogues of the Payne-P\\\u0027olya-Weinberger, Hile-Protter, and Yang eigenvalue inequalities for the Schr\\\"odinger operator on arbitrary finite subsets of the integer lattice $\\mathbb{Z}^n$. The results extend known inequalities for the discrete Laplacian to a more general class of Schr\\\"odinger operators with nonnegative potentials and weighted eigenvalue problems.",
    "arxiv_id": "2601.10523",
    "authors": [
      "Wentao Liu"
    ],
    "categories": [
      "math.SP"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "Some Eigenvalue Inequalities for the Schr\\\"odinger Operator on Integer Lattices",
    "url": "https://arxiv.org/abs/2601.10523",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "0188dc1f-4680-4e18-807e-f9822525b05e",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}