{
  "abstract": "Let $A_ρ$ be the coordinate ring of the projective line over $\\Fq$ with a closed point of degree $N$ removed. We give finite formulas for higher Weil operators in a basis of Riemann--Roch spaces, which recover the formulas of Hu--Ou--Yang when $N=1$. We identifythese operators with representatives of the residue Casimir tensors and obtain a determinant formula for the Weil pairing, relative to a chosen determinant realization. For a normalized rank-one Drinfeld module, we compute the remainder of its Anderson generating function modulo any nonconstant $p\\in A_ρ$. The formula includes multiple zeros and a zero at the ordinary point at infinity. Its last coefficient is a nonzero scalar multiple of an exponential division value. When $(p)$ is a finite principal prime, a value of the associated special function at one zero of $p$ generates the torsion field after adjoining that zero. We give an explicit $q$-linear formula recovering a torsion generator from this value. We also specialize the evaluation theorem of Gazda--Maurischat and compute the different as the principal ideal $(\\partial_xp)$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41131",
  "author_total": 3,
  "authors": [
    {
      "name": "Chuangqiang Hu"
    },
    {
      "name": "Xiao-Min Huang"
    },
    {
      "name": "Guorui Ma"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/57037dcmkzm7v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41131",
  "fulltext_url": null,
  "id": "57037dcmkzm7v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41131",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41131",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/57037dcmkzm7v.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41131",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41131"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Weil Operators and Remainders of Anderson Generating Functions over a Punctured Projective Line",
  "title_text": "Weil Operators and Remainders of Anderson Generating Functions over a Punctured Projective Line",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/57037dcmkzm7v",
  "venue": "arXiv",
  "versions": []
}