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Computational Methods and Function Theory
Article
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arXiv.org e-Print Archive
Preprint . 2005
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Computational Methods and Function Theory
Article . 2006 . Peer-reviewed
License: Springer TDM
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zbMATH Open
Article . 2006
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https://dx.doi.org/10.48550/ar...
Article . 2005
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Article
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Claim

Bloch’s Principle

Bloch's principle
descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jun 2006Embargo end date: 01 Jan 2005 English Publisher:Springer Science and Business Media LLCJournal:Computational Methods and Function Theory, volume 6, pages 77-108 (issn: 1617-9447, eissn: 2195-3724, Copyright policy )
Authors: Bergweiler, Walter;

doi: 10.1007/bf03321119 , 10.48550/arxiv.math/0511048

arXiv: math/0511048

Bloch’s Principle

Abstract

A heuristic principle attributed to A. Bloch says that a family of holomorphic functions is likely to be normal if there is no nonconstant entire functions with this property. We discuss this principle and survey recent results that have been obtained in connection with it. We pay special attention to properties related to exceptional values of derivatives and existence of fixed points and periodic points, but we also discuss some other instances of the principle.

30 pages

Related Organizations
Keywords

Mathematics - Complex Variables, execptional value, 30D45, Value distribution of meromorphic functions of one complex variable, Nevanlinna theory, normal family, periodic point, fixed point, Entire functions of one complex variable (general theory), Mathematics - Classical Analysis and ODEs, quasinormal, Bloch's principle, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Normal functions of one complex variable, normal families, Complex Variables (math.CV)

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    popularity
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    influence
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
46
Top 10%
Top 10%
Top 10%
Green
bronze