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## ON COMMON BOREL DIRECTIONS OF MEROMORPHIC FUNCTIONS OF INFINITE ORDER

Xiao Xiuzhi
G. Polya has proved the following theorem: suppose that G(Z) is an entire function of infinite order. If the order of G(Z) attains that of the entire complex plane, in any arbitary small angular domain whose bisector is some direction arg Z=_0, then arg Z=_0 is Julia direction of G(Z). In this article a characteristic theorem of Borel direction of meromorphic functions of infinite order is established, based on R. Nevanlinna's fundamental inequality for angular domains. It may be applied to common Borel direction of the functions and their multiple values, of the constants and "low order" functions, of the functions and their derivatives. One of the main theorems is: Theorem. Among the meromorphic functions of infinite order of the complex plane, any function f(Z) and it's reciprocal 1/(f(Z)) have at least one, it's Borel direction of the order p(r) with Borel direction of the order p(r) of the derivative is common.
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 【Citations】
 Chinese Journal Full-text Database 1 Hits
 1 He Yuzan(Institute of mathematics, Academia Sinica);ON THE MULTIPLE VALUES OF ALGEBROID FUNCTIONS[J];Acta Mathematica Sinica;1979-06
 【Co-citations】
 Chinese Journal Full-text Database 5 Hits
 1 XUAN Zu-xing~1,QIN Shu-lan~2(1.Basic Courses Department of Beijing Union University,Beijing 100101,China;2.Department of Science,Qingdao Binhai University,Qingdao Shandong 266555,China);On Uniqueness of Entire Algebroid Functions[J];Journal of Beijing Union University(Natural Sciences);2009-01 2 He Yuzan(Institute of Mathematics Academia Sinica Beijing, China);A UNIQUENESS THEOREM OF ALGEBROID FUNCTIONS AND SYSTEMS OF HOLOMORPHIC FUNCTIONS[J];Pure and Applied Mathematics;1985-00 3 Xie Huichun;On the Multiple Values of Meromorphic Functions and Uniqueness.[J];Journal of Fujian Normal University(Natural Science Edition);1983-01 4 Wu Guirong (Department of Mathematics,Fujian Teachers University, Fuzhou 350007);On the Multiple Values and Uniqueness for Meromorphic Functions[J];JOURNAL OF FUJIAN TEACHERS UNIVERSITY(NATURAL SCIENCE);1998-04 5 Yi Hongxun (Shandong University);On the Multiple Values and Uniqueness of Algebroid Functions[J];Chinese Journal of Engineering Mathematics;1991-04
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