Some results on entire functions of finite lower order. (English) Zbl 0813.30026

Let \(f(z)\) be an entire function of order \(\lambda\) and of finite lower order \(\mu\). If the zeros of \(f(z)\) accumulate in the vicinity of a finite number of rays, then (i) \(\lambda\) is finite; (ii) for any \(k_ 1> 1\), there exists \(k_ 2> 1\), such that \(T(k_ 1 r,f)\leq k_ 2 T(r, f)\) for all \(r\geq r_ 0\).
Applying the above results, the author proves some theorems and simplifies some proofs of the theorems of Yang Lo [Trans. Am. Math. Soc. 308, No. 2, 583-601 (1988; Zbl 0653.30022)] and Zhang Guanghuo [The theory of entire and meromorphic functions (1993; Zbl 0790.30017)] on the relations among the lower order, Borel directions, the deficient values and asymptotic values.


30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
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