{
  "annotation_id": "f7a29166-55c8-4aee-8d65-1519d9ec71dc",
  "date_created": "2026-02-17T05:53:24.265000Z",
  "date_modified": "2026-02-17T05:53:24.265000Z",
  "file_hash": "26bfc9263c8bec48aa079c6e6947c1617d3876695b005136570d31e99fb0badc",
  "private": false,
  "record": {
    "abstract": "The well-known Zalcman conjecture, which implies the Bieberbach conjecture, states that the coefficients of univalent functions $f(z) = z + \\sum\\limits_2^{\\infty} a_n z^n$ on the unit disk satisfy $|a_n^2 - a_{2n-1}| \\le (n-1)^2$ for all $n \u003e 2$, with equality only for the Koebe function and its rotations. The conjecture was proved by the author for $n \\le 6$ (using geometric arguments related to the Ahlfors-Schwarz lemma) and remains open for $n \\ge 7$.\n  The main theorem of this paper states that these conjectures are equivalent and provides their simultaneous proof for all $n \\ge 3$ combining the indicated geometric arguments with a new author\u0027s approach to extremal problems for holomorphic functions based on lifting the rotationally homogeneous coefficient functionals to the Bers fiber space over universal Teichmuller space.",
    "arxiv_id": "2601.10584",
    "authors": [
      "Samuel L. Krushkal"
    ],
    "categories": [
      "math.CV"
    ],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "title": "On Zalcman\u0027s and Bieberbach conjectures",
    "url": "https://arxiv.org/abs/2601.10584",
    "version": "v1"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "96e62362-ae1a-48c9-9524-e6ba5f172720",
    "id": "arXiv Dataset",
    "type": "Model",
    "variant": "snapshot-2026-01-17",
    "version": "0.1.0"
  },
  "user_id": 1000002
}