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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Normality and exceptional values of derivatives


Author: Walter Bergweiler
Journal: Proc. Amer. Math. Soc. 129 (2001), 121-129
MSC (1991): Primary 30D45, 30D30
Published electronically: June 21, 2000
MathSciNet review: 1695100
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Abstract:

We show that a family $\mathcal{F}$ of functions meromorphic in some domain is normal, if for all $f\in\mathcal{F}$ the derivative $f'$ omits the value $1$ and if the values that $f'$ can take at the zeros of $f$ satisfy certain restrictions. As an application we obtain a new proof of a theorem of Langley which classifies the functions $f$ meromorphic in the plane such that $f$ and $f''$ have no zeros.


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Additional Information

Walter Bergweiler
Affiliation: Mathematisches Seminar, Christian–Albrechts–Universität zu Kiel, Ludewig–Meyn–Str. 4, D–24098 Kiel, Germany
Email: bergweiler@math.uni-kiel.de

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05477-0
PII: S 0002-9939(00)05477-0
Received by editor(s): January 5, 1999
Received by editor(s) in revised form: March 9, 1999
Published electronically: June 21, 2000
Communicated by: Albert Baernstein II
Article copyright: © Copyright 2000 American Mathematical Society



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