{
  "id": "2211.05747",
  "version": "v1",
  "published": "2022-11-10T18:26:13.000Z",
  "updated": "2022-11-10T18:26:13.000Z",
  "title": "Lower Bounds for Rankin-Selberg $L$-functions on the Edge of the Critical Strip",
  "authors": [
    "Qiao Zhang"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $F$ be a number field, and let $\\pi_1$ and $\\pi_2$ be distinct unitary cuspidal automorphic representations of $\\operatorname{GL}_{n_1}(\\mathbb{A}_F)$ and $\\operatorname{GL}_{n_2}(\\mathbb{A}_F)$ respectively. In this paper, we derive new lower bounds for the Rankin-Selberg $L$-function $L(s, \\pi_1 \\times \\widetilde{\\pi}_2)$ along the edge $\\Re s = 1$ of the critical strip in the $t$-aspect. The corresponding zero-free region for $L(s, \\pi_1 \\times \\widetilde{\\pi}_2)$ is also determined.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-11-10T18:26:13.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11M26",
      "11F66"
    ],
    "keywords": [
      "lower bounds",
      "critical strip",
      "rankin-selberg",
      "distinct unitary cuspidal automorphic representations",
      "corresponding zero-free region"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}