{
  "id": "2406.13013",
  "version": "v1",
  "published": "2024-06-18T19:10:05.000Z",
  "updated": "2024-06-18T19:10:05.000Z",
  "title": "An uniform lower bound for classical Kloosterman sums and an application",
  "authors": [
    "Jewel Mahajan",
    "Jishu Das",
    "Stephan Baier"
  ],
  "comment": "11 pages",
  "categories": [
    "math.NT"
  ],
  "abstract": "We present an elementary uniform lower bound for the classical Kloosterman sum $S(a,b;c)$ under the condition of its non-vanishing and $(ab,c)=1$, with $c$ being an odd integer. We then apply this lower bound for Kloosterman sums to derive an explicit lower bound in the Petersson's trace formula, subject to a pertinent condition. Consequently, we achieve a modified version of a theorem by Jung and Sardari, wherein the parameters $k$ and $N$ are permitted to vary independently.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-18T19:10:05.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L05",
      "11L07",
      "11F72"
    ],
    "keywords": [
      "classical kloosterman sum",
      "elementary uniform lower bound",
      "application",
      "peterssons trace formula",
      "explicit lower bound"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 11,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}