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Schlicht Dirichlet Series
Published online by Cambridge University Press: 20 November 2018
Extract
For power series
(1.1) for which
(1.2),
it has been known for four decades (1) that ƒ(z) is regular and univalent or schlicht in |z| < 1. This theorem, due to J. W. Alexander, has more recently been studied by Remak (5) who has shown that w = ƒ(z), under the hypothesis (1.2), maps |z| < 1 onto a star-like region, and if (1.2) is not satisfied=(z) need not be univalent in |z| < 1 for a proper choice of the amplitudes of the coefficients an.
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- Copyright © Canadian Mathematical Society 1958
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