{
  "id": "1907.03145",
  "version": "v1",
  "published": "2019-07-06T15:57:16.000Z",
  "updated": "2019-07-06T15:57:16.000Z",
  "title": "On diagonal equations over finite fields via walks in NEPS of graphs",
  "authors": [
    "Denis E. Videla"
  ],
  "comment": "8 pages",
  "categories": [
    "math.CO",
    "math.NT"
  ],
  "abstract": "In this paper, we find a formula for the number of $r$-walks on NEPS of arbitrary graphs in any basis. We apply this formula to find the number of elements of a commutative ring that can be represented as a sum of $r$ units. We then also obtain the number of solutions $(x_i)_{i=1}^r$ with $x_i\\neq 0$ to the diagonal equation $x_{1}^k+\\cdots+x_{r}^k=b$ over a finite field $\\mathbb{F}_{p^m}$, obtaining an identity for generalized Jacobi sums.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-07-06T15:57:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "05C25"
    ],
    "keywords": [
      "finite field",
      "diagonal equation",
      "generalized jacobi sums",
      "arbitrary graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}