The Eremenko–Lyubich constant

Rempe, Lasse ORCID: 0000-0001-8032-8580 (2023) The Eremenko–Lyubich constant. Bulletin of the London Mathematical Society, 55 (1). pp. 113-118.

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Official URL: http://dx.doi.org/10.1112/blms.12714

Abstract

Eremenko and Lyubich proved that an entire function (Formula presented.) whose set of singular values is bounded is expanding at points where (Formula presented.) is large. These expansion properties have been at the centre of the subsequent study of this class of functions, now called the Eremenko–Lyubich class. We improve the estimate of Eremenko and Lyubich, and show that the new estimate is asymptotically optimal. As a corollary, we obtain an elementary proof that functions in the Eremenko–Lyubich class have lower order at least (Formula presented.).

Item Type:	Article
Divisions:	Faculty of Science and Engineering > School of Physical Sciences
Depositing User:	Symplectic Admin
Date Deposited:	09 Aug 2022 08:31
Last Modified:	09 Mar 2023 05:59
DOI:	10.1112/blms.12714
Open Access URL:	https://doi.org/10.1112/blms.12714
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3160779