EMIS ELibM Electronic Journals PUBLICATIONS DE L'INSTITUT MATHEMATIQUE (BEOGRAD) (N.S.)
Vol. 75(89), pp. 185–197 (2004)

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ON THE ZEROS OF FUNCTIONS IN THE BERS SPACE

A. Fletcher and V. Markovic

Mathematics Institute, University of Warwick, Coventry, CV4 7AL, United Kingdom

Abstract: We present some results on the distribution of zeros of functions in the Bers space $Q(\mathbb{D})$, showing how the distribution depends on the bounds of the growth of $|f(z)|$ as $|z|\to1$, for $f\in Q(\mathbb{D})$. We also exhibit an open and dense subset, $M\subset Q(\mathbb{D})$, which has the property of uniform control over the number of zeros in disks of hyperbolic radius 1 contained in $\mathbb{D}$.

Classification (MSC2000): 30C15; 30F30

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