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A contact and coefficient correction for Korenblum's constant

Primarily AI-generated textHuman understanding: some partsmath.CV — Complex Variables

Contributed by Ricardo Pinho ↗

Version 1 / Oct 31, 2026 / CC BY 4.0

Abstract

Retaining an angular deficit in an annular coefficient estimate gives C68≥0.44667C_{68}\ge0.44667 for Korenblum's constant in the unweighted Bergman space. The flux input is David Niedbala Giraudin's. A contact-moment estimate and an even outer factor retain a correction involving the first two coefficients; a rational measure then satisfies the modified moment conditions. The argument builds on Wang's coefficient approach and Wikström's moment integration. This note is unrefereed, with no independent human review or formalization.

Provenance statement

Analysis and proof drafting by AI agents under my direction; I reviewed the results at summary level. AI agents also prepared certificates, checking software, and publication materials. No line-by-line human verification is claimed. AI is not an author.

References

  1. D. Niedbala Giraudin, Korenblum flux and enclosing estimates, PR 274; https://github.com/teorth/optimizationproblems/pull/274.link
  2. C. Wang, Domination in the Bergman space and Korenblum's constant, Integral Equations and Operator Theory 61 (2008), 423--432, https://doi.org/10.1007/s00020-008-1587-4; A lower bound on Korenblum's constant, Proceedings of the American Mathematical Society 153 (2025), 1209--1214, https://doi.org/10.1090/proc/17112.DOI
  3. F. Wikström, Moment duality and an improved lower bound for Korenblum's constant, Lemma 3.1 (moment integration); https://arxiv.org/abs/2607.17748.link
  4. R. Pinho, earlier covering-strip coefficient construction and references to Wang and Schuster; https://github.com/rpinho/korenblum-c68-certificate.link
  5. R. Pinho, Korenblum C68 certificate , contact-spectral , revision placeholder COMMIT_C68 ; https://github.com/rpinho/korenblum-c68-certificate/tree/a8bfa25da9b07f0a7b8fefcd5043c0547855c9d1/contact-spectral.link

Version history

  1. v1Submitted by Ricardo PinhoInitial depositCurrentOct 30, 2026