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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 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Normality and exceptional values of derivatives
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by Walter Bergweiler PDF
Proc. Amer. Math. Soc. 129 (2001), 121-129 Request permission

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
  • MR Author ID: 35350
  • Email: bergweiler@math.uni-kiel.de
  • 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
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 121-129
  • MSC (1991): Primary 30D45, 30D30
  • DOI: https://doi.org/10.1090/S0002-9939-00-05477-0
  • MathSciNet review: 1695100