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关于亚纯函数的亏量与特征函数 被引量:5

SUM OF DEFICIENCIES OF MEROMORPHIC FUNCTION AND ITS CHARACTERISTIC FUNCTION
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摘要 设f(z)为开平面上的有穷级亚纯函数,如果som form n=∑δ(a,f)=2,则有如下结果成立。(ⅰ)当δ(∞,f)=1时,对所有正整数k有 T(r,f)~T(r,f^(k)),r→∞。(ⅱ)当δ(∞,f)=0时 T(r,f^(k))~(k+1)T(r,f),r→∞。 Let f(z) be a meromorphic function of finite order, if sum from α to δ(α, f)=2, we have the following results. (1) If δ(∞, f)=1, then for every positive integer k, T(r, f)~T(r, f^((h))), as r→∞. (2) If δ(∞, f)=0, then T(r, f^((h)))~(k+1)T(r, f), as r→∞.
作者 杨连中
机构地区 山东大学数学系
出处 《山东大学学报(自然科学版)》 CSCD 1989年第1期7-11,共5页 Journal of Shandong University(Natural Science Edition)
关键词 亚纯函数 特征函数 亏量 亏值 meromorphic function, characteristic function, deficiency, deficient value
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参考文献1

  • 1Xiong Qinglai,Chinese Mathematics,1967年,9卷,146页

同被引文献18

  • 1Ziegler Hans J W. Vector valued Nevanlinna theory [M] .Boston:Pitman( Advanced Publishing Program) ,1982.
  • 2Hu Chuangan,Hu Qijian. The Nevanlinna、theorems for aclass [ J]. Complex Var Elliptic Equ,2006,51 (8) :777-791.
  • 3Singh S K, Gopalakrishna H S. Exceptional values of anentire and meromorphic functions [ J]. Math Ann, 1971,191(2) :121-142.
  • 4Edrei A. Sums of deficiencies of meromorphic functions II[J].J Analyse Math, 1967,19( 14) :79-107.
  • 5Weitsman Allen. Meromorphic functions with maximal de-ficiency sum and a conjecture of F. Nevanlinna [ J]. ActaMath, 1969,123(1) :115-139.
  • 6Singh S K f Kulkami V N. Characteristc function of a mero-morphic function and its derivative [ J]. Ann Polo Math,1973,28(1) :123-133.
  • 7Xuan Zuxing, Wu Nan. On the Nevanlinna's theory forvector-valued mappings [ J]. Abstr Appl Anal,2010( 1/2/3/4):1-15.
  • 8Wu Zhaojun,Xuan Zuxing. Milloux inequality of ?-valuedmeromorphic function [ J]. The Scientific World Journal,2014:861573,7.
  • 9Wu Zhaojun, Chen Yuxian. ^-valued meromorphic func-tions with maximal deficiency sum [ J]. Applied Mathe-matics ?-Notes ,2013,13(1) :141-147.
  • 10Wu Zhaojun, Xuan Zuxing. Deficiency and relative defi-ciency of -valued meromorphic functions [ J ]. AppliedMathematics ?.-Notes,2013,13( 1) : 100-108.

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