Open Access
Feb. 2003 On a conjecture of W. Bergweiler
Wei-Chuan Lin, Hong-Xun Yi
Proc. Japan Acad. Ser. A Math. Sci. 79(2): 23-27 (Feb. 2003). DOI: 10.3792/pjaa.79.23


In this paper it is discussed for which meromorphic functions $f$ the homogeneous differential $f(z) f''(z) - a(f'(z))^2$ has only finitely many zeros. It is shown that any transcendental meromorphic functions $f(z)$ have the form $R(z) \exp(P(z))$ for a rational function $R$ and a polynomial $P$ with the property if $a \ne 1, (n \pm 1) / n$, $n \in N$. This result settles one conjecture proposed by W. Bergweiler.


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Wei-Chuan Lin. Hong-Xun Yi. "On a conjecture of W. Bergweiler." Proc. Japan Acad. Ser. A Math. Sci. 79 (2) 23 - 27, Feb. 2003.


Published: Feb. 2003
First available in Project Euclid: 18 May 2005

zbMATH: 1056.30032
MathSciNet: MR1960738
Digital Object Identifier: 10.3792/pjaa.79.23

Primary: 30D35
Secondary: 30D30 , 30D45

Keywords: differential polynomial , meromorphic function , normal family

Rights: Copyright © 2003 The Japan Academy

Vol.79 • No. 2 • Feb. 2003
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