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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Bloch constants for meromorphic functions near an isolated singularity
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by David Minda
Proc. Amer. Math. Soc. 91 (1984), 69-72
DOI: https://doi.org/10.1090/S0002-9939-1984-0735566-6
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Abstract:

Suppose $f$ is meromorphic in a punctured neighborhood of the origin and has an essential singularity at the origin. Given any $\varepsilon > 0$ we show that the Riemann surface of $f$ contains an unramified disk of spherical radius $\pi /3 - \varepsilon$. The number $\pi /3$ can be replaced by $\pi /2$ if $f$ is locally schlicht and this value is best possible. If $f$ is actually holomorphic, then the Riemann surface of $f$ contains arbitrarily large unramified euclidean disks. These results generalize theorems of Valiron and Ahlfors dealing with holomorphic and meromorphic functions, respectively, on the complex plane which have an essential singularity at infinity.
References
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Bibliographic Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 91 (1984), 69-72
  • MSC: Primary 30C25; Secondary 30D99
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0735566-6
  • MathSciNet review: 735566