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

Langley, J.K.

Abstract

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.

Citation

Langley, J. (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
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 141
• Issue: 1
• Pages: 225-246
• DOI: https://doi.org/10.1007/s11854-020-0115-6
• Keywords: General Mathematics; Analysis
• 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