{
  "id": "0909.2387",
  "version": "v1",
  "published": "2009-09-13T02:33:27.000Z",
  "updated": "2009-09-13T02:33:27.000Z",
  "title": "On the transcendence of some infinite sums",
  "authors": [
    "Pingzhi Yuan",
    "Juan Li"
  ],
  "comment": "15pages",
  "doi": "10.1112/jlms/jdp029",
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper we investigate the infinite convergent sum $T=\\sum_{n=0}^\\infty\\frac{P(n)}{Q(n)}$, where $P(x)\\in\\bar{\\mathbb{Q}}[x]$, $Q(x)\\in\\mathbb{Q}[x]$ and $Q(x)$ has only simple rational zeros. N. Saradha and R. Tijdeman have obtained sufficient and necessary conditions for the transcendence of $T$ if the degree of $Q(x)$ is 3. In this paper we give sufficient and necessary conditions for the transcendence of $T$ if the degree of $Q(x)$ is 4 and $Q(x)$ is reduced.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2009-09-13T02:33:27.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11J81",
      "11J86",
      "11J91"
    ],
    "keywords": [
      "infinite sums",
      "transcendence",
      "necessary conditions",
      "infinite convergent sum",
      "simple rational zeros"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0909.2387Y"
    }
  }
}