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Eremenko's Conjecture for Functions with Real Zeros: The Role of the Minimum Modulus

Nicks, Daniel; Rippon, Philip and Stallard, Gwyneth (2020). Eremenko's Conjecture for Functions with Real Zeros: The Role of the Minimum Modulus. International Mathematics Research Notices (Early access).

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DOI (Digital Object Identifier) Link: https://doi.org/10.1093/imrn/rnaa020
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Abstract

We consider the class of real transcendental entire functions $f$ of finite order with only real zeros, and show that if the iterated minimum modulus tends to $\infty$, then the escaping set $I(f)$ of $f$ has the structure of a spider's web, in which case Eremenko's conjecture holds. This minimum modulus condition is much weaker than that used in previous work on Eremenko's conjecture. For functions in this class we analyse the possible behaviours of the iterated minimum modulus in relation to the order of the function $f$.

Item Type: Journal Item
Copyright Holders: 2020 The Authors
ISSN: 1687-0247
Project Funding Details:
Funded Project NameProject IDFunding Body
Baker's conjecture and Eremenko's conjecture: a unified approach (XM-08-066-GS)EP/H006591/1EPSRC (Engineering and Physical Sciences Research Council)
Keywords: transcendental entire function; escaping set; Eremenko's conjecture; spider's web; minimum modulus; order; genus; deficiency
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Related URLs:
Item ID: 69153
Depositing User: Philip Rippon
Date Deposited: 27 Jan 2020 10:07
Last Modified: 24 Jun 2020 21:05
URI: http://oro.open.ac.uk/id/eprint/69153
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