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Growth of functions in cercles de remplissage
Published online by Cambridge University Press: 09 April 2009
Abstract
Suppose that f is meromorphic in the plane, and that there is a sequence Zn → ∞ and a sequence of positive numbers ∈n → 0, such that ∈n|zn|f#(zn)/log|zn| → ∞. It is shown that if f is analytic and non-zero in the closed discs Δn = {z: |z – zn| ≦∈n|zn|}, n = 1, 2, 3 …, then, given any positive integer K, there are arbitrarily large values of n and there is a point z in Δn such that │f (z)| 〉 |Z│k. Examples are given to show that the hypotheses cannot be relaxed.
MSC classification
- Type
- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 72 , Issue 1 , February 2002 , pp. 131 - 136
- Copyright
- Copyright © Australian Mathematical Society 2002
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