Julia directions of meromorphic functions and their derivatives |
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Authors: | A. Sauer |
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Affiliation: | 1.Fachbereich Mathematik, Gerhard-Mercator-Universit?t Duisburg, Lotharstr. 65, D-46047 Duisburg, Germany,? e-mail: sauer@math.uni-duisburg.de,Germany |
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Abstract: | ![]() We prove that if a transcendental meromorphic function has no Julia direction and is bounded on a path to ¥ infty then there is a common Julia direction for all derivatives. Related statements are obtained under the assumption that f is o(?{ | z | }) o(sqrt{mid z mid}) or O(?{ | z | }) O(sqrt{mid z mid}) on a path to ¥ infty . Further we disprove a conjecture of Frank and Wang by means of a counterexample. |
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