{
  "id": "1805.09225",
  "version": "v1",
  "published": "2018-05-23T15:32:39.000Z",
  "updated": "2018-05-23T15:32:39.000Z",
  "title": "A general family of congruences for Eisenstein series",
  "authors": [
    "Su Hu",
    "Min-Soo Kim",
    "Min Sha"
  ],
  "comment": "15 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, based on Serre's $p$-adic family of Eisenstein series, we prove a general family of congruences for Eisenstein series $G_k$ in the form $$ \\sum_{i=1}^n g_i(p)G_{f_i(p)}\\equiv g_0(p)\\mod p^N $$ where $f_1(t),\\ldots,f_n(t)\\in\\mathbb{Z}[t]$ are non-constant integer polynomials with positive leading coefficients and $g_0(t),\\ldots,g_n(t)\\in\\mathbb{Q}(t)$ are rational functions. This generalizes the classical von Staudt-Clausen's and Kummer's congruences of Eisenstein series.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-05-23T15:32:39.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "eisenstein series",
      "general family",
      "non-constant integer polynomials",
      "classical von staudt-clausens",
      "rational functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}