{
  "id": "1804.06402",
  "version": "v1",
  "published": "2018-04-17T17:59:02.000Z",
  "updated": "2018-04-17T17:59:02.000Z",
  "title": "Zeros of Rankin-Selberg $L$-functions at the edge of the critical strip",
  "authors": [
    "Jesse Thorner",
    "Asif Zaman"
  ],
  "comment": "40 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $\\pi$ and $\\pi_0$ be unitary cuspidal automorphic representations. We prove log-free zero density estimates for Rankin-Selberg $L$-functions of the form $L(s,\\pi\\times\\pi_0)$, where $\\pi$ varies in a given family and $\\pi_0$ is fixed. These estimates are unconditional in many cases of interest; they hold in full generality assuming an average form of the generalized Ramanujan conjecture. We consider applications of these estimates related to mass equidistribution for Hecke-Maass forms, the rarity of Landau-Siegel zeros of Rankin-Selberg $L$-functions, the Chebotarev density theorem, and $\\ell$-torsion in class groups of number fields.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-04-17T17:59:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "critical strip",
      "rankin-selberg",
      "log-free zero density estimates",
      "unitary cuspidal automorphic representations",
      "chebotarev density theorem"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}