Open Access
November 2009 On new singular directions of some Schröder functions
Nan Wu, Zu-Xing Xuan
Proc. Japan Acad. Ser. A Math. Sci. 85(9): 123-128 (November 2009). DOI: 10.3792/pjaa.85.123


In this paper, we study the Hayman T directions and the precise Borel directions of maximal kind of meromorphic solutions f(z) of the Schröder equations f(sz)=R(f(z)), where |s|<1 and R(w) is a rational function with $\deg [R]\geq 2$. We will show that, if $\operatorname {arg}[s]/2\pi \notin Q$, then f(z) has any direction as Hayman T direction and maximus Borel direction as well. This is a continue work of [Ishizaki, K. and Yanaihara, N., Borel and Julia directions of meromorphic Schröder functions, Math. Proc. Camb. Phil. Soc. 139 (2005), 139-147.] and [Yuan, W.J., Qi, J.M. and Seiki Mori. Singular directions of meromorphic solutions of some non-autonomous Schröder equations, Complex Analysis and its Applications Proceedings of the 15th ICFIDCAA held in Osaka (Japan), July 30-August 3, 2007].


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Nan Wu. Zu-Xing Xuan. "On new singular directions of some Schröder functions." Proc. Japan Acad. Ser. A Math. Sci. 85 (9) 123 - 128, November 2009.


Published: November 2009
First available in Project Euclid: 5 November 2009

zbMATH: 1190.30024
MathSciNet: MR2573960
Digital Object Identifier: 10.3792/pjaa.85.123

Primary: 30D10
Secondary: 30B10 , 30D20 , 34M05

Keywords: Borel direction of maximal kind , Hayman $T$ direction , Schröder function

Rights: Copyright © 2009 The Japan Academy

Vol.85 • No. 9 • November 2009
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