{
  "abstract": "For every prime power $q$, we determine the $a$-number of the Serre-type maximal curves $X(q,n)$: $y^{q^2}-y=x^{(q^n+1)/(q+1)}$ over $\\mathbb{F}_{q^{2n}}$, $n\\ge 3$ odd, introduced by Abdón, Bezerra and Quoos as a generalization of Serre's curve $y^4+y=x^3$ over $\\mathbb{F}_{64}$. The Weierstrass semigroup at the unique point at infinity gives an explicit basis of holomorphic differentials, on which the Cartier operator acts by monomials; this reduces the $a$-number to a lattice-point count, which we evaluate in closed form.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15266",
  "author_total": 1,
  "authors": [
    {
      "name": "Mahyar Shafighi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6239dbs9sy8t1.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15266",
  "fulltext_url": null,
  "id": "6239dbs9sy8t1",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15266",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.AG"
    ],
    [
      "openalex",
      "2608|Algebraic Geometry and Number Theory"
    ]
  ],
  "openalex": "W7221778578",
  "pdf_url": "https://arxiv.org/pdf/2610.15266",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6239dbs9sy8t1.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15266",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15266"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AG",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "The a-number of the Serre-type maximal curves of Abdón-Bezerra-Quoos",
  "title_text": "The a-number of the Serre-type maximal curves of Abdón-Bezerra-Quoos",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/6239dbs9sy8t1",
  "venue": "arXiv",
  "versions": []
}