# Iterating the minimum modulus: functions of order half, minimal type

Nicks, Daniel; Rippon, Philip and Stallard, Gwyneth (2021). Iterating the minimum modulus: functions of order half, minimal type. Computational Methods and Function Theory (Early Access).

## Abstract

For a transcendental entire function , the property that there exists such that as , where , is related to conjectures of Eremenko and of Baker, for both of which order minimal type is a significant rate of growth. We show that this property holds for functions of order minimal type if the maximum modulus of has sufficiently regular growth and we give examples to show the sharpness of our results by using a recent generalisation of Kjellberg's method of constructing entire functions of small growth, which allows rather precise control of .

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