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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information


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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 30D45, 30D30

Retrieve articles in all journals with MSC (1991): 30D45, 30D30

Additional Information

Walter Bergweiler
Affiliation: Mathematisches Seminar, Christian–Albrechts–Universität zu Kiel, Ludewig–Meyn–Str. 4, D–24098 Kiel, Germany

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