Nevanlinna theory of meromorphic functions on annuli
type: Item
instance of: scholarly article
title: Nevanlinna theory of meromorphic functions on annuli
zbMATH Open document ID: 1193.30044
author: Zhuan Ye
author: Mark E. Lund
published in: Science China. Mathematics
publication date: 2010-05-26T00:00:00Z
review text: In this survey paper, the recent development of Nevanlinna theory of meromorphic functions on annuli is discussed. As the authors mention, this development is motivated historically by its applications to study of growth properties of a solution of complex differential equations, e.g., [\textit{Y. M. Chiang} and \textit{I. Laine}, Jap. J. Math., New Ser. 24, No. 2, 367--402 (1998; Zbl 0918.34040)]. Systematic studies on the annuli \(\{z: 1/R_0<|z|< R_0, 1< R_0\leq+\infty\}\) are found in e.g., [\textit{A. Kondratyuk} and \textit{I. Laine}, Meromorphic functions in multiply connected domains, Fourier series methods in complex analysis. Proceedings of the workshop, 2005. Joensuu: University of Joensuu, Department of Mathematics. Report Series. Department of Mathematics, University of Joensuu 10, 9--111 (2006; Zbl 1144.30013)], in which a number of counterparts of classical theorems in the Nevanlinna theory for meromorphic functions are proved. In Section 2, definitions of Nevanlinna functions in annuli are given. Nevanlinna's first fundamental theorem in annuli and Nevanlinna's logarithmic derivatives lemma in annuli are stated in Sections 3 and 4, respectively. The counterparts of other classical theorems, for examples Clunie-type lemmas and the five values theorem are mentioned in Section 5. In Section 6, one of the tools for the proofs so called Valiron's decomposition lemma is stated. At the end of the paper, the authors state open questions on growth of composite functions and on sequences of annuli.
reviewed by: Katsuya Ishizaki
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 5712100
zbMATH Keywords: Nevanlinna theory in annuli
zbMATH Keywords: meromorphic functions
zbMATH Keywords: Valiron's decomposition lemma
MaRDI profile type: Publication
full work available at URL: s11425-010-0037-3
OpenAlex ID: W2007706351
cites work: Q3037791
cites work: Q5737219
cites work: Q2716042
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cites work: On the Nevanlinna theory for meromorphic functions on annuli. I.
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DOI: 10.1007/S11425-010-0037-3
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description: scientific article; zbMATH DE number 5712100