Advanced Studies in Pure Mathematics

Singular directions of meromorphic solutions of some non-autonomous Schröder equations

Katsuya Ishizaki and Niro Yanagihara

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Abstract

Let $s = |s| e^{2\pi \lambda i}$ be a complex constant satisfying $|s| \gt 1$ and $\lambda \notin \mathbb{Q}$. We show that for a transcendental meromorphic solution $f(z)$ of some non-autonomous Schröder equation $f(sz) = R(z, f(z))$, any direction is a Borel direction.

Article information

Source
Potential Theory in Matsue, H. Aikawa, T. Kumagai, Y. Mizuta and N. Suzuki, eds. (Tokyo: Mathematical Society of Japan, 2006), 155-166

Dates
Received: 25 March 2005
Revised: 9 June 2005
First available in Project Euclid: 16 December 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1544999687

Digital Object Identifier
doi:10.2969/aspm/04410155

Subjects
Primary: 30D35: Distribution of values, Nevanlinna theory
Secondary: 39B32: Equations for complex functions [See also 30D05]

Keywords
Schröder equation Nevanlinna theory Borel direction Value distribution theory in angular domains

Citation

Ishizaki, Katsuya; Yanagihara, Niro. Singular directions of meromorphic solutions of some non-autonomous Schröder equations. Potential Theory in Matsue, 155--166, Mathematical Society of Japan, Tokyo, Japan, 2006. doi:10.2969/aspm/04410155. https://projecteuclid.org/euclid.aspm/1544999687


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