{
  "id": "1809.01841",
  "version": "v1",
  "published": "2018-09-06T06:19:34.000Z",
  "updated": "2018-09-06T06:19:34.000Z",
  "title": "A vanishing criterion for Dirichlet series with periodic coefficients",
  "authors": [
    "Tapas Chatterjee",
    "M. Ram Murty",
    "Siddhi Pathak"
  ],
  "journal": "Contemp. Math., 701, 69--80, Amer. Math. Soc., Providence, RI, 2018",
  "categories": [
    "math.NT"
  ],
  "abstract": "We address the question of non-vanishing of $L(1,f)$ where $f$ is an algebraic-valued, periodic arithmetical function. We do this by characterizing algebraic-valued, periodic functions $f$ for which $L(1,f)=0$. The case of odd functions was resolved by Baker, Birch and Wirsing in 1973. We apply a result of Bass to obtain a characterization for the even functions. We also describe a theorem of the first two authors which says that it is enough to consider only the even and the odd functions in order to obtain a complete characterization.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-09-06T06:19:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M20"
    ],
    "keywords": [
      "dirichlet series",
      "periodic coefficients",
      "vanishing criterion",
      "odd functions",
      "periodic arithmetical function"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}