Composite Bank-Laine functions and a question of Rubel

Langley, J.

doi:10.1090/S0002-9947-01-02917-8

Composite Bank-Laine functions and a question of Rubel
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by J. K. Langley PDF

Trans. Amer. Math. Soc. 354 (2002), 1177-1191 Request permission

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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