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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.

##### MSC:
 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory
##### Keywords:
lower order; Borel directions; deficient values
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##### References:
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