{
  "id": "1305.2813",
  "version": "v1",
  "published": "2013-05-13T15:39:56.000Z",
  "updated": "2013-05-13T15:39:56.000Z",
  "title": "On mod $p$ singular modular forms",
  "authors": [
    "Siegfried Böcherer",
    "Toshiyuki Kikuta"
  ],
  "comment": "21 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We show that an elliptic modular form with integral Fourier coefficients in a number field $K$, for which all but finitely many coefficients are divisible by a prime ideal $\\frak{p}$ of $K$, is a constant modulo $\\frak{p}$. A similar property also holds for Siegel modular forms. Moreover, we define the notion of mod $\\frak{p}$ singular modular forms and discuss some relations between their weights and the corresponding prime $p$. We discuss some examples of mod $\\frak{p}$ singular modular forms arising from Eisenstein series and from theta series attached to lattices with automorphisms. Finally, we apply our results to properties mod $\\frak{p}$ of Klingen-Eisenstein series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-13T15:39:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F33",
      "11F46"
    ],
    "keywords": [
      "elliptic modular form",
      "integral fourier coefficients",
      "siegel modular forms",
      "klingen-eisenstein series",
      "properties mod"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.2813B"
    }
  }
}