Normality and exceptional values of derivatives
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- by Walter Bergweiler PDF
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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.References
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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