{
  "id": "math/0412224",
  "version": "v1",
  "published": "2004-12-11T20:09:36.000Z",
  "updated": "2004-12-11T20:09:36.000Z",
  "title": "A relation between the zeros of different two $L$-functions which have the Euler product and functional equation",
  "authors": [
    "Masatoshi Suzuki"
  ],
  "comment": "29 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "As automorphic $L$-functions or Artin $L$-functions, several classes of $L$-functions have Euler products and functional equations. In this paper we study the zeros of $L$-functions which have the Euler products and functional equations. We show that there exists some relation between the zeros of the Riemann zeta-function and the zeros of such $L$-functions. As a special case of our results, we find the relations between the zeros of the Riemann zeta-function and the zeros of automorphic $L$-functions attached to elliptic modular forms or the zeros of Rankin-Selberg $L$-functions attached to two elliptic modular forms.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-12-11T20:09:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M41"
    ],
    "keywords": [
      "functional equation",
      "euler product",
      "elliptic modular forms",
      "riemann zeta-function",
      "automorphic"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 29,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math.....12224S"
    }
  }
}