Bounded meromorphic functions on the complex 2-disc

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Abstract

We describe bounded, holomorphic functions on the complex 2-disc that admit a meromorphic extension to a larger 2-disc. This solves a conjecture of Bickel, Knese, Pascoe and Sola. The key technical ingredient is an old theorem of Zariski about integrally closed ideals in 2-dimensional regular rings.

Original languageEnglish (US)
Pages (from-to)1-7
Number of pages7
JournalPeriodica Mathematica Hungarica
Volume88
Issue number1
DOIs
StatePublished - Mar 2024

All Science Journal Classification (ASJC) codes

  • General Mathematics

Keywords

  • Integral closure
  • Meromorphic function
  • Polydisc

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