{
  "id": "2012.01969",
  "version": "v1",
  "published": "2020-12-03T14:50:02.000Z",
  "updated": "2020-12-03T14:50:02.000Z",
  "title": "A new generalization of the Genocchi numbers and its consequence on the Bernoulli polynomials",
  "authors": [
    "Bakir Farhi"
  ],
  "comment": "12 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "This paper presents a new generalization of the Genocchi numbers and the Genocchi theorem. As consequences, we obtain some important families of integer-valued polynomials those are closely related to the Bernoulli polynomials. Denoting by ${(B_n)}_{n \\in \\mathbb{N}}$ the sequence of the Bernoulli numbers and by ${(B_n(X))}_{n \\in \\mathbb{N}}$ the sequence of the Bernoulli polynomials, we especially obtain that for any natural number $n$, the reciprocal polynomial of the polynomial $\\big(B_n(X) - B_n\\big)$ is integer-valued.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-03T14:50:02.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11B68",
      "13F20",
      "13F25",
      "11C08"
    ],
    "keywords": [
      "bernoulli polynomials",
      "genocchi numbers",
      "generalization",
      "consequence",
      "bernoulli numbers"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 12,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}