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A sharp growth condition for a fast escaping spider’s web

Rippon, P. J. and Stallard, G. M. (2013). A sharp growth condition for a fast escaping spider’s web. Advances in Mathematics, 244 pp. 337–353.

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DOI (Digital Object Identifier) Link: https://doi.org/10.1016/j.aim.2013.04.021
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Abstract

We show that the fast escaping set A(f) of a transcendental entire function f has a structure known as a spider’s web whenever the maximum modulus of f grows below a certain rate. The proof uses a new local version of the cos πρ theorem, based on a comparatively unknown result of Beurling. We also give examples of entire functions for which the fast escaping set is not a spider’s web which show that this growth rate is sharp. These are the first examples for which the escaping set has a spider’s web structure but the fast escaping set does not. Our results give new insight into possible approaches to proving a conjecture of Baker, and also a conjecture of Eremenko.

Item Type: Journal Item
Copyright Holders: 2013 Published by Elsevier Inc.
ISSN: 1090-2082
Project Funding Details:
Funded Project NameProject IDFunding Body
Baker's conjecture and Eremenko's conjecture: a unified approach.EP/H006591/1EPSRC (Engineering and Physical Sciences Research Council)
Keywords: fast escaping set; spiders’ webs; cos πρ theorem
Academic Unit/School: Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM)
Item ID: 37990
Depositing User: Philip Rippon
Date Deposited: 11 Jul 2013 08:22
Last Modified: 11 Dec 2018 20:07
URI: http://oro.open.ac.uk/id/eprint/37990
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