{
  "id": "2003.12868",
  "version": "v1",
  "published": "2020-03-28T18:47:14.000Z",
  "updated": "2020-03-28T18:47:14.000Z",
  "title": "Hasse Polynomials of L-functions of Certain Exponential Sums",
  "authors": [
    "Chao Chen"
  ],
  "categories": [
    "math.NT"
  ],
  "abstract": "In this paper, we focus on computing the higher slope Hasse polynomials of L-functions of certain exponential sums associated to the following family of Laurent polynomials $f(x_1,\\ldots ,x_{n+1})=\\sum_{i=1}^na_i x_{n+1}\\left(x_i+\\frac{1}{x_i}\\right)+a_{n+1} x_{n+1}+\\frac{1}{x_{n+1}}$, where $a_i \\in \\F^*_{q}$, $i=1,2, \\ldots, n+1$. We find a simple formula for the Hasse polynomial of the slope one side and study the irreducibility of these Hasse polynomials. We will also provide a simple form of all the higher slope Hasse polynomials for $n=3$, answering an open question of Zhang and Feng.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-03-28T18:47:14.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11S40",
      "11T23",
      "11L07"
    ],
    "keywords": [
      "exponential sums",
      "higher slope hasse polynomials",
      "l-functions",
      "open question",
      "simple formula"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}