Deficient values and angular distribution of entire functions. (English) Zbl 0653.30022

Yang, Lo

Trans. Am. Math. Soc. 308, No. 2, 583-601 (1988).

Theorem. Let f(z) be an entire function of lower order \(\mu\), \(0<\mu <\infty\). If \(q<\infty\) is the number of Borel directions of order \(\geq \mu\) of f(z) and \(P_ j\) \((j=0,-1,-2,...)\) is the number of finite, non- zero deficient values of \(f^{(j)}(z)\) \([=a\) primitive of order \(| j|\) of f(z)], then \(\sum^{\infty}_{j=0}P_ j\leq 2\mu\).

Reviewer: W.H.J.Fuchs

MSC:

30D35	Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
30D20	Entire functions of one complex variable (general theory)

Keywords:

Borel directions; deficient values

References:

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