{
  "id": "2102.04837",
  "version": "v1",
  "published": "2021-02-09T14:26:36.000Z",
  "updated": "2021-02-09T14:26:36.000Z",
  "title": "Discrete and zeta-regularized determinants of the Laplacian on polygonal domains with Dirichlet boundary conditions",
  "authors": [
    "Rafael Leon Greenblatt"
  ],
  "comment": "35 pages, 6 figures",
  "categories": [
    "math-ph",
    "math.FA",
    "math.MP",
    "math.PR"
  ],
  "abstract": "For $\\Pi \\subset \\mathbb{R}^2$ a connected, open, bounded set whose boundary is a finite union of polygons whose vertices have integer coordinates, the logarithm of the discrete Laplacian on $L\\Pi \\cap \\mathbb{Z}^2$ with Dirichlet boundary conditions has an asymptotic expansion for large $L$ in which the term of order 1 is the logarithm of the zeta-regularized determinant of the corresponding continuum Laplacian. When $\\Pi$ is not simply connected, this result extends to Laplacians acting on two-valued functions with a specified monodromy class.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-02-09T14:26:36.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "dirichlet boundary conditions",
      "zeta-regularized determinant",
      "polygonal domains",
      "result extends",
      "finite union"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 35,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}