{
  "id": "2207.12439",
  "version": "v1",
  "published": "2022-07-25T18:00:31.000Z",
  "updated": "2022-07-25T18:00:31.000Z",
  "title": "Equidistribution and independence of Gauss sums",
  "authors": [
    "Antonio Rojas-León"
  ],
  "categories": [
    "math.NT",
    "math.AG"
  ],
  "abstract": "We prove a general independent equidistribution result for Gauss sums associated to $n$ monomials in $r$ variable multiplicative characters over a finite field, which generalizes several previous equidistribution results for Gauss and Jacobi sums. As an application, we show that any relation satisfied by these Gauss sums must be a combination of the conjugation relation $G(\\chi)G(\\overline\\chi)=\\pm q$, Galois conjugation invariance and the Hasse-Davenport product formula.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-07-25T18:00:31.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "11L05",
      "11L07",
      "11T24"
    ],
    "keywords": [
      "gauss sums",
      "general independent equidistribution result",
      "independence",
      "hasse-davenport product formula",
      "galois conjugation invariance"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}