{
  "id": "1810.02134",
  "version": "v1",
  "published": "2018-10-04T10:11:51.000Z",
  "updated": "2018-10-04T10:11:51.000Z",
  "title": "On higher congruences between cusp forms and Eisenstein series. II",
  "authors": [
    "Bartosz Naskręcki"
  ],
  "comment": "20 pages",
  "journal": "Notes from the International School on Computational Number Theory; Izmir Institute of Technology 2017, (Engin B\\''uy\\''ukaik and Ilker Inam, editors), Springer Birkh\\''auser",
  "categories": [
    "math.NT"
  ],
  "abstract": "We study congruences between cuspidal modular forms and Eisenstein series at levels which are square-free integers and for equal even weights. This generalizes our previous results from Naskr\\k{e}cki [17] for prime levels and provides further evidence for the sharp bounds obtained under restrictive ramification conditions. We prove an upper bound on the exponent in the general square-free situation and also discuss the existence of the congruences when the coefficients belong to the rational numbers and weight equals 2.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-04T10:11:51.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "eisenstein series",
      "higher congruences",
      "cusp forms",
      "cuspidal modular forms",
      "general square-free situation"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}