Transactions of the American Mathematical Society

Author(s): J. K. Langley
Journal: Trans. Amer. Math. Soc. 354 (2002), 1177-1191.
MSC (2000): Primary 30D35; Secondary 34M05
Posted: October 24, 2001
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Abstract: A Bank-Laine function is an entire function

satisfying $E'(z) = \pm 1$ at every zero of

. We determine all Bank-Laine functions of form $E = f \circ g$ , with

entire. Further, we prove that if

is a transcendental entire function of finite order, then there exists a path tending to infinity on which

and all its derivatives tend to infinity, thus establishing for finite order a conjecture of Rubel.

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Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 30D35, 34M05

J. K. Langley
Affiliation: School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
Email: jkl@maths.nott.ac.uk

DOI: 10.1090/S0002-9947-01-02917-8
PII: S 0002-9947(01)02917-8
Received by editor(s): June 12, 2000
Posted: October 24, 2001
Dedicated: Dedicated to the memory of Steve Bank and Lee Rubel
Copyright of article: Copyright 2001, American Mathematical Society

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