{
  "id": "2212.14620",
  "version": "v1",
  "published": "2022-12-30T10:13:58.000Z",
  "updated": "2022-12-30T10:13:58.000Z",
  "title": "Second moment of degree three $L$-functions",
  "authors": [
    "Sampurna Pal"
  ],
  "comment": "First Draft",
  "categories": [
    "math.NT"
  ],
  "abstract": "Let $F$ be a Hecke-Maass cusp form for $SL(3,\\mathbb{Z})$. We obtain a non-trivial upper bound for the second moment of $L(F,s)$ in $t$-aspect: $$\\int_{T}^{2T}|L(F,1/2+it)|^2 dt\\ll_{F,\\epsilon} T^{3/2-3/1676+\\epsilon}.$$",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-12-30T10:13:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11F66",
      "11M99"
    ],
    "keywords": [
      "second moment",
      "hecke-maass cusp form",
      "non-trivial upper bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}