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Bank-Laine functions via quasiconformal surgery. (English) Zbl 1158.30019

Rippon, Philip J. (ed.) et al., Transcendental dynamics and complex analysis. In honour of Noel Baker. Cambridge: Cambridge University Press (ISBN 978-0-521-68372-2/pbk). London Mathematical Society Lecture Note Series 348, 165-178 (2008).
Using quasiconformal surgery, the authors construct new examples of entire functions \(E(z)\) such that \(E(z)=0\) implies \(E'(z)=\pm 1,\) these associated with second order linear differential equations with transcendental coefficients, where \(f_1,f_2\) are linearly independent solutions of the equation \(w''+A(z)w=0\), and \(E=f_1f_2\) is a Bank-Laine function and satisfies \[ 4A=(E'/E)^2-2E''/E-1/E^2. \] They also extend some previous results on the zero sequences of such functions.
For the entire collection see [Zbl 1143.30002].

MSC:

30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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