The size of Wiman–Valiron discs for subharmonic functions of a certain type

FENTON, P.C. and LINGHAM, Eleanor (2016). The size of Wiman–Valiron discs for subharmonic functions of a certain type. Complex Variables and Elliptic Equations, 61 (4), 456-468. [Article]

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Abstract
Wiman–Valiron theory and the results of Macintyre about “flat regions” describe the asymptotic behaviour of entire functions in certain discs around maximum points. We use a technique of Bergweiler, Rippon and Stallard to describe the asymptotic behaviour of a certain type of subharmonic function, and a technique of Bergweiler to estimate the size of its Wiman–Valiron discs from above and below. The results are extended to -subharmonic functions.
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