{
  "abstract": "Let $\\F_q$ be the field of order $q = p^f$ for prime $p$. If $G(χ)$ is the Gauss sum attached to a multiplicative character $χ$ on $\\F_q^\\times$, then $G(χ) = G(χ^p)$. We investigate the converse question: when does the equality of Gauss sums $G(χ_2) = G(χ_1)$ imply that $χ_2 = χ_1^{p^j}$ for some integer $j$. If $χ_2 = χ_1^{p^j}$, we say that $χ_1$ and $χ_2$ are Frobenius-conjugate. We use the Stickelberger factorization of ideals in cyclotomic fields to give an easily testable criterion for equality of Gauss sums, based on $p$-adic digit expansion. As an application, we develop several conditions under which Gauss sum equalities between characters on $\\F_q^\\times$ are explained by Frobenius-conjugacy. For example, if $χ_1$ has order $q-1$ or $\\frac{1}{2}(q-1)$ and $G(χ_2) = G(χ_1)$, then $χ_1$ and $χ_2$ are Frobenius-conjugate. We also include several examples, based on the explicit evaluation of certain {\\em pure} Gauss sums by R.J. Evans.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.28211",
  "author_total": 4,
  "authors": [
    {
      "name": "Moshe Adrian"
    },
    {
      "name": "Jack Diamond"
    },
    {
      "name": "Kenneth Kramer"
    },
    {
      "name": "Geo Kam-Fai Tam"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eg3ky68zdteyg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.28211",
  "fulltext_url": null,
  "id": "eg3ky68zdteyg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.28211",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2602|Analytic Number Theory Research"
    ]
  ],
  "openalex": "W7214159525",
  "pdf_url": "https://arxiv.org/pdf/2609.28211",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eg3ky68zdteyg.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:00Z",
      "native_id": "2609.28211",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.28211"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Distinguishing Gauss sums",
  "title_text": "Distinguishing Gauss sums",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:00Z",
  "url": "https://research.draconitic.com/paper/eg3ky68zdteyg",
  "venue": "arXiv",
  "versions": []
}