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The Möbius pseudodistance of the annulus and an improved lower bound for Korenblum's constant

Primarily AI-generated textHuman understanding: no partsmath.CV — Complex Variablesmath.FA — Functional Analysis

Contributed by David Niedbala Giraudin ↗

Version 1 / Nov 02, 2026 / CC BY 4.0

Abstract

We show that Korenblum's constant of the Bergman space satisfies c2≥0.446c_2\ge 0.446. The best published lower bound was c2≥0.4263c_2\ge 0.4263 (Wikström, 2026). The new ingredient is a closed form, in Jacobi theta functions, of the Möbius pseudodistance of the annulus {c<∣z∣<1}\{c<|z|<1\} between two points of the same centred circle. It separates the variables and yields three monotonicity properties, one of which, a profile inequality, combined with Kirszbraun's theorem in the hyperbolic plane, improves the constant in Wang's annular estimate. Wikström's dual moment criterion is then verified at c=223/500c=223/500 for an explicit measure with fourteen rational atoms, in rigorous arithmetic, by a self-contained verifier. The French version of this note is dated 21 October 2026.

Provenance statement

Mathematical content, LaTeX source and verifier produced with Claude (Anthropic) under the author's direction. French original dated 21 October 2026 (OpenTimestamps); English version 1 November 2026.

Tools used

Anthropic
Claude Opus

References

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Show all 12 referencesShow fewer references
  1. C. Wang, A lower bound on Korenblum's constant , Proc.\ Amer.\ Math.\ Soc.\ 153 (2025), 1209--1214.
  2. F. Wikström, Moment duality and an improved lower bound for Korenblum's constant , arXiv:2607.17748 (2026).arXiv

Version history

  1. v1 · 5 pagesSubmitted by David Niedbala GiraudinInitial depositCurrentNov 01, 2026