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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Deficient values and angular distribution of entire functions


Author: Lo Yang
Journal: Trans. Amer. Math. Soc. 308 (1988), 583-601
MSC: Primary 30D35; Secondary 30D30
DOI: https://doi.org/10.1090/S0002-9947-1988-0930073-8
MathSciNet review: 930073
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Abstract: Let $ f(z)$ be an entire function of positive and finite order $ \mu $. If $ f(z)$ has a finite number of Borel directions of order $ \geqslant \mu $, then the sum of numbers of finite nonzero deficient values of $ f(z)$ and all its primitives does not exceed $ 2\mu $. The proof is based on several lemmas and application of harmonic measure.


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DOI: https://doi.org/10.1090/S0002-9947-1988-0930073-8
Article copyright: © Copyright 1988 American Mathematical Society