Bank-Laine functions with real zeros

Langley, J K

Abstract

Suppose that E is a real entire function of finite order with zeros which are all real but neither bounded above nor bounded below, such that E (z) = ±1 whenever E(z) = 0. Then either E has an explicit representation in terms of trigonometric functions or the zeros of E have exponent of convergence at least 3. An example constructed via quasiconformal surgery demonstrates the sharpness of this result.

Citation

Langley, J. K. (2020). Bank-Laine functions with real zeros. Computational Methods and Function Theory, 20, 653-665. https://doi.org/10.1007/s40315-020-00342-9

• Journal Article Type: Article
• Acceptance Date: Jul 19, 2020
• Online Publication Date: Sep 24, 2020
• Publication Date: Sep 24, 2020
• Deposit Date: Jul 21, 2020
• Publicly Available Date: Sep 25, 2021
• Journal: Computational Methods and Function Theory
• Print ISSN: 1617-9447
• Publisher: Springer Verlag
• Peer Reviewed: Peer Reviewed
• Volume: 20
• Pages: 653-665
• DOI: https://doi.org/10.1007/s40315-020-00342-9
• Keywords: Bank-Laine function; entire function; zeros MSC 2010: 30D20; 30D35
• Public URL: https://nottingham-repository.worktribe.com/output/4780913
• Publisher URL: https://link.springer.com/article/10.1007/s40315-020-00342-9