{
  "abstract": "We extend recent work of the author over $\\mathbb{Z}$ into the positive characteristic setting of $\\mathbb{F}_q[t]$. In particular, for a polynomial $F \\in \\mathbb{F}_q[t]$ of degree $N$, let $R_k(α)$ denote the exponential sum over $k$-free polynomials $f$ with $\\text{deg}(f-F)<K$. For all $s>0$, we prove essentially tight upper and lower bounds for the $s$-th moment of $R_k(α)$ whenever $K > (\\frac{1}{2}+ε)N$, and in even shorter intervals when $s>1+\\frac{1}{k}$. As an application of these results, we prove a lower bound of order $q^{\\frac{K}{6}}$ for the $L^1$-mean of the Möbius-twisted exponential sum over $\\mathbb{F}_q[t]$ whenever $K >(\\frac{1}{2}+ε)N$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.30942",
  "author_total": 1,
  "authors": [
    {
      "name": "Ben Doyle"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ddt6gwzqqg4dz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.30942",
  "fulltext_url": null,
  "id": "ddt6gwzqqg4dz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.30942",
  "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": "W7204896758",
  "pdf_url": "https://arxiv.org/pdf/2608.30942",
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-31",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ddt6gwzqqg4dz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:48Z",
      "native_id": "2608.30942",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.30942"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Subconvexity of Short $k$-Free Exponential Sums in $\\mathbb{F}_q[t]$",
  "title_text": "Subconvexity of Short k-Free Exponential Sums in 𝔽_q[t]",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:48Z",
  "url": "https://research.draconitic.com/paper/ddt6gwzqqg4dz",
  "venue": "arXiv",
  "versions": []
}