Value distribution of Painleve transcendents of the first and the second kind

被引：6
|
作者：
Shimomura, S [1 ]
机构：
[1] Keio Univ, Dept Math, Yokohama, Kanagawa 2238522, Japan
来源：
JOURNAL D ANALYSE MATHEMATIQUE | 2000年 / 82卷 / 1期
关键词：
Meromorphic Function; Simple Zero; Meromorphic Solution; Linear Ordinary Differential Equation; Transcendental Meromorphic Function;
D O I：
10.1007/BF02791233
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We examine value distribution properties of the first and the second Painleve transcendents. For every transcendental meromorphic solution phi (z) (resp. psi (z)) of the first (resp. second) Painleve equation, the deficiency delta (g, phi) (resp. delta (g, psi)) of a small function g(z) does not exceed 1/2. Furthermore, for phi (z), the ramification index satisfies v(g, phi) less than or equal to 5/12.
引用
收藏
页码：333 / 346
页数：14
相关论文
共 50 条
  • [21] On the value distribution of f+a(f′)n
    Fang MingLiang
    Zalcman, Lawrence
    SCIENCE IN CHINA SERIES A-MATHEMATICS, 2008, 51 (07): : 1196 - 1202
  • [22] Some results on the value distribution of differential polynomials
    Fan, Jinyu
    Xiao, Jianbin
    Fang, Mingliang
    OPEN MATHEMATICS, 2023, 21 (01):
  • [23] Two results on the value distribution of meromorphic functions
    Yang, Degui
    He, Zhiying
    Liu, Dan
    OPEN MATHEMATICS, 2024, 22 (01):
  • [24] ANGULAR VALUE DISTRIBUTION CONCERNING SHARED VALUES
    Pan, Biao
    Lin, Weichuan
    ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, 2015, 45 (06) : 1919 - 1935
  • [25] On the value distribution of differential polynomials of meromorphic functions
    Xu, Yan
    Qiu, Huiling
    ANNALES POLONICI MATHEMATICI, 2010, 98 (03) : 283 - 289
  • [26] VALUE DISTRIBUTION OF DIFFERENCE OPERATOR ON MEROMORPHIC FUNCTIONS
    Ding, Jie
    Yang, Lian-Zhong
    BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2014, 51 (05) : 1291 - 1297
  • [27] Value distribution theory and the research of Yang Lo
    HAYMAN W. K.
    Science China(Mathematics), 2010, 53 (03) : 513 - 522
  • [28] On the Value Distribution of fn f(k)-1
    Karmakar, Himadri
    Sahoo, Pulak
    RESULTS IN MATHEMATICS, 2018, 73 (03)
  • [29] On value distribution of f (k)-af n
    Zhang Z.
    Frontiers of Mathematics in China, 2006, 1 (4) : 612 - 619
  • [30] Value Distribution of Differential Polynomials in Meromorphic Functions
    LIU Xiao-shu (Department of Mathematics
    数学季刊, 2006, (02) : 297 - 300
12345