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Composite Bank-Laine functions and a question of Rubel


Author: J. K. Langley
Journal: Trans. Amer. Math. Soc. 354 (2002), 1177-1191
MSC (2000): Primary 30D35; Secondary 34M05
DOI: https://doi.org/10.1090/S0002-9947-01-02917-8
Published electronically: October 24, 2001
MathSciNet review: 1867377
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Abstract: A Bank-Laine function is an entire function $E$ satisfying $E'(z) = \pm 1$ at every zero of $E$. We determine all Bank-Laine functions of form $E = f \circ g$, with $f, g$ entire. Further, we prove that if $h$ is a transcendental entire function of finite order, then there exists a path tending to infinity on which $h$ and all its derivatives tend to infinity, thus establishing for finite order a conjecture of Rubel.


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Additional Information

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

DOI: https://doi.org/10.1090/S0002-9947-01-02917-8
Received by editor(s): June 12, 2000
Published electronically: October 24, 2001
Dedicated: Dedicated to the memory of Steve Bank and Lee Rubel
Article copyright: © Copyright 2001 American Mathematical Society

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