Deficient values and angular distribution of entire functions

Yang, Lo

doi:10.1090/S0002-9947-1988-0930073-8

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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