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Meromorphic Functions with Radially Distributed Values

In: Value Distribution of Meromorphic Functions

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  • Jianhua Zheng

    (Tsinghua University, Department of Mathematical Sciences)

Abstract

A value on the extended complex plane is a radially distributed value of a transcendental meromorphic function if most of points at which the value is assumed distribute closely along a finite number of rays from the origin. In this chapter, we study the growth order of a meromorphic function with two radially distributed values and a distinct deficient value (in other words, this hints a condition under which deficient values do not exist). We respectively treat two cases: one is without assumption about the growth of the function considered and the other is under assumption of the function being of the finite lower order. The Nevanlinna characteristic for an angle plays crucial role in the investigation of this subject. Actually, the idea to study this subject is the following: the Nevanlinna characteristic T(r, f) for |z|

Suggested Citation

  • Jianhua Zheng, 2010. "Meromorphic Functions with Radially Distributed Values," Springer Books, in: Value Distribution of Meromorphic Functions, chapter 0, pages 207-228, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-12909-4_5
    DOI: 10.1007/978-3-642-12909-4_5
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