Meromorphic Functions with Radially Distributed Values

Jianhua Zheng ()
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Jianhua Zheng: Tsinghua University, Department of Mathematical Sciences

Chapter Chapter 5 in Value Distribution of Meromorphic Functions, 2010, pp 207-228 from Springer

Abstract: 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|

Keywords: Angle Nevanlinna characteristic; Growth order; Radially distributed value (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-642-12909-4_5

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DOI: 10.1007/978-3-642-12909-4_5

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