{
  "annotation_id": "9be05068-6a62-4987-8dc4-c7d03d55830a",
  "date_created": "2026-02-17T05:53:19.899000Z",
  "date_modified": "2026-02-17T05:53:19.899000Z",
  "file_hash": "d1dfad69cfcbcb09922384d8f65bd205d18755c86ddf6036fa80ba6f8e4b3a63",
  "private": false,
  "record": {
    "abstract": "The shape of a number field $K$ of degree $n$ is defined as the equivalence class of the lattice of integers with respect to linear operations that are composites of rotations, reflections, and positive scalar dilations. The shape is a point in the space of shapes $\\mathscr{S}_{n-1}$, which is the double quotient $\\mathrm{GL}_{n-1}(\\mathbb{Z}) \\backslash \\mathrm{GL}_{n-1}(\\mathbb{R}) / \\mathrm{GO}_{n-1}(\\mathbb{R})$. We investigate the distribution of shapes of pure sextic number fields $K=\\mathbb{Q}(\\sqrt[6]{m})$, ordered by absolute discriminant. Such fields are partitioned into $20$ distinct Types determined by local conditions at $2$ and $3$, and an explicit integral basis is given in each case. For each Type, the shape of $K$ admits an explicit description in terms of shape parameters. Fixing the sign of $m$ and a Type, we prove that the corresponding shapes are equidistributed along a translated torus orbit in the space of shapes. The limiting distribution is given by an explicit measure expressed as the product of a continuous measure and a discrete measure.",
    "arxiv_id": "2601.09411",
    "authors": [
      "Anuj Jakhar",
      "Ravi Kalwaniya",
      "Anwesh Ray",
      "Bidisha Roy"
    ],
    "categories": [
      "math.NT"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "title": "On the distribution of shapes of sextic pure number fields",
    "url": "https://arxiv.org/abs/2601.09411",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5cc0cb83-aafa-44ae-b4a8-e83533dfd6b1",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}