Bounded meromorphic functions on the complex 2-disc

János Kollár

doi:10.1007/s10998-023-00538-1

Bounded meromorphic functions on the complex 2-disc

János Kollár

Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 language	English (US)
Pages (from-to)	1-7
Number of pages	7
Journal	Periodica Mathematica Hungarica
Volume	88
Issue number	1
DOIs	https://doi.org/10.1007/s10998-023-00538-1
State	Published - Mar 2024

All Science Journal Classification (ASJC) codes

General Mathematics

Keywords

Integral closure
Meromorphic function
Polydisc

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10.1007/s10998-023-00538-1

Cite this

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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.",

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N2 - 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.

AB - 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.

KW - Integral closure

KW - Meromorphic function

KW - Polydisc

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Bounded meromorphic functions on the complex 2-disc

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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