Pith Number

pith:DU7YUXDI

pith:2026:DU7YUXDIEPWUIKMZ6AY33AKZ4P

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Sharp multiplier estimates for the higher-order Schwarzian derivatives of the Koebe function

Jianjun Jin

The Koebe function achieves the sharp multiplier norms for its higher-order Schwarzian derivatives between weighted Bergman spaces.

arxiv:2604.20326 v5 · 2026-04-22 · math.CV

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\usepackage{pith}
\pithnumber{DU7YUXDIEPWUIKMZ6AY33AKZ4P}

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Record completeness

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The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Claims

C1strongest claim

We establish sharp multiplier estimates for the higher-order Schwarzian derivatives of the Koebe function.

C2weakest assumption

The proof relies on an explicit formula for the higher-order Schwarzian derivatives of the Koebe function and a recent theorem from our earlier work.

C3one line summary

Sharp multiplier estimates are established for the higher-order Schwarzian derivatives of the Koebe function in weighted Bergman spaces.

Receipt and verification

First computed	2026-05-20T00:03:12.157975Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

1d3f8a5c6823ed442999f031bd8159e3e27044b2dcef22ac21a917b34f4bc0b9

Aliases

arxiv: 2604.20326 · arxiv_version: 2604.20326v5 · doi: 10.48550/arxiv.2604.20326 · pith_short_12: DU7YUXDIEPWU · pith_short_16: DU7YUXDIEPWUIKMZ · pith_short_8: DU7YUXDI

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/DU7YUXDIEPWUIKMZ6AY33AKZ4P \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 1d3f8a5c6823ed442999f031bd8159e3e27044b2dcef22ac21a917b34f4bc0b9

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "a238ea1fc19c93f791a804718067f09520e6e8d65c922bc5e7172e2648210a4c",
    "cross_cats_sorted": [],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.CV",
    "submitted_at": "2026-04-22T08:21:23Z",
    "title_canon_sha256": "bea6a55f7454002f4fced5c03c92e44122b3e0f7bc46389f95b68721e6d2661e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "2604.20326",
    "kind": "arxiv",
    "version": 5
  }
}