On Subharmonic and Entire Functions of Small Order: After Kjellberg

Rippon, Philip J. and Stallard, Gwyneth M. (2021). On Subharmonic and Entire Functions of Small Order: After Kjellberg. International Mathematics Research Notices, 2021(18) pp. 14267–14295.

DOI: https://doi.org/10.1093/imrn/rnab060

Abstract

We give a general method for constructing examples of transcendental entire functions of given small order, which allows precise control over the size and shape of the set where the minimum modulus of the function is relatively large. Our method involves a novel technique to obtain an upper bound for the growth of a positive harmonic function defined in a certain type of multiply connected domain, based on comparing the Harnack metric and hyperbolic metric, which gives a sharp estimate for the growth in many cases.

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About

• Item ORO ID
• 76142
• Item Type
• Journal Item
• ISSN
• 1687-0247
• Project Funding Details

• Funded Project Name	Project ID	Funding Body
  Classifying Wandering Domains	EP/R010560/1	EPSRC (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 or School
• Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
  Faculty of Science, Technology, Engineering and Mathematics (STEM)
• Copyright Holders
• © 2021 Philip J. Rippon, © 2021 Gwyneth M. Stallard
• Depositing User
• Philip Rippon