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

Langley, James K.

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Authors

James K. Langley



Abstract

The Bank–Laine conjecture concerning the oscillation of solutions of second order homogeneous linear differential equations has recently been disproved by Bergweiler and Eremenko. 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.

Citation

Langley, J. K. (2020). Bank–Laine functions, the Liouville transformation and the Eremenko–Lyubich class. Journal d'Analyse Mathématique, 141(1), 225-246. https://doi.org/10.1007/s11854-020-0115-6

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
Peer Reviewed Peer Reviewed
Volume 141
Issue 1
Pages 225-246
DOI https://doi.org/10.1007/s11854-020-0115-6
Public URL https://nottingham-repository.worktribe.com/output/1441685
Publisher URL https://link.springer.com/article/10.1007/s11854-020-0115-6
Additional Information Received: 16 October 2018; Revised: 30 November 2018; First Online: 12 November 2020

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