{
  "id": "1501.04185",
  "version": "v1",
  "published": "2015-01-17T10:23:43.000Z",
  "updated": "2015-01-17T10:23:43.000Z",
  "title": "On a conjecture of Erdös and certain Dirichlet series",
  "authors": [
    "Tapas Chatterjee",
    "M. Ram Murty"
  ],
  "comment": "To appear in the Pacific Journal of Mathematics",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $f:\\Z/q\\Z\\rightarrow\\Z$ be such that $f(a)=\\pm 1$ for $1\\le a<q$, and $f(q)=0$. Then Erd\\\"os conjectured that $\\sum_{n\\ge1}\\frac{f(n)}{n} \\ne 0$. For $q$ even, this is trivially true. If $q\\equiv 3$ ( mod $4$), Murty and Saradha proved the conjecture. We show that this conjecture is true for $82\\%$ of the remaining integers $q\\equiv 1$ ( mod $4$).",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-01-17T10:23:43.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M06",
      "11M41",
      "11M20"
    ],
    "keywords": [
      "dirichlet series",
      "conjecture",
      "trivially true"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150104185C"
    }
  }
}