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Bank–Laine functions, the Liouville transformation and the Eremenko–Lyubich class

Langley, J.K.


J.K. Langley


The Bank-Laine conjecture concerning the oscillation of solutions of second order homogeneous linear differential equations has recently been disproved by Bergweiler and Ere-menko. It is shown here, however, that the conjecture is true if the set of finite critical and asymptotic values of the coefficient function is bounded. It is also shown that if E is a Bank-Laine function of finite order with infinitely many zeros, all real and positive, then its zeros must have exponent of convergence at least 3/2, and an example is constructed via quasiconformal surgery to demonstrate that this result is sharp. MSC 2000: 30D35.


Langley, J. (2020). Bank–Laine functions, the Liouville transformation and the Eremenko–Lyubich class. Journal d'Analyse Mathématique, 141(1), 225-246.

Journal Article Type Article
Acceptance Date Dec 14, 2018
Online Publication Date Nov 12, 2020
Publication Date 2020-09
Deposit Date Jan 3, 2019
Publicly Available Date Oct 1, 2021
Journal Journal d'Analyse Mathématique
Print ISSN 0021-7670
Electronic ISSN 1565-8538
Publisher Springer Verlag
Peer Reviewed Peer Reviewed
Volume 141
Issue 1
Pages 225-246
Keywords General Mathematics; Analysis
Public URL
Publisher URL
Additional Information Received: 16 October 2018; Revised: 30 November 2018; First Online: 12 November 2020


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