与其导数具有公共值的代数体函数的唯一性定理

数学物理学报 ›› 2011, Vol. 31 ›› Issue (5): 1335-1344.

与其导数具有公共值的代数体函数的唯一性定理

刘慧芳¹, 孙道椿²

1.江西师范大学数学与信息科学学院 |南昌 330022|2.华南师范大学数学科学学院 |广州 |510631

收稿日期:2009-09-06 修回日期:2010-11-11 出版日期:2011-10-25 发布日期:2011-10-25
基金资助:
国家自然科学基金(10871076)和江西省教育厅科技项目(GJJ09150)资助

Uniqueness Theorems for Algebroid Functions Sharing Values with Their Derivatives

LIU Hui-Fang¹, SUN Dao-Chun²

1.Institute of Mathematics and Informatics, Jiangxi Normal University, Nanchang 330022;
2. School of Mathematics, South China Normal University, Guangzhou 510631

Received:2009-09-06 Revised:2010-11-11 Online:2011-10-25 Published:2011-10-25
Supported by:
国家自然科学基金(10871076)和江西省教育厅科技项目(GJJ09150)资助

摘要/Abstract

摘要：

该文定义了代数体函数与其导数的公共值, 并得到了几个关于代数体函数与其导数具有公共值的唯一性定理.

关键词: 代数体函数, 函数元素, 公共值, 唯一性

Abstract:

In this paper, the shared value of algebroid functions and their derivatives are defined. Some uniqueness theorems of algebroid functions sharing values with their derivatives are obtained.

Key words: Algebroid function, Function element, Shared value, Uniqueness

中图分类号:

30D35

刘慧芳, 孙道椿. 与其导数具有公共值的代数体函数的唯一性定理[J]. 数学物理学报, 2011, 31(5): 1335-1344.

LIU Hui-Fang, SUN Dao-Chun. Uniqueness Theorems for Algebroid Functions Sharing Values with Their Derivatives[J]. Acta mathematica scientia,Series A, 2011, 31(5): 1335-1344.

[1] Nevanlinna R. Le Théorème de Picard-Borel et la Théorie des Fonctions Méromorphes. Paris: Gauthiers-Villars, 1929

[2] Yang C C, Yi H X. Uniqueness Theory of Meromorphic Functions. Beijing: Science Press, 2003; New York: Kluwer Academic Publishers, 2003

[3] Valiron G. Sur la dérivée des fonctions algébroïdes. Bull Soc Math, 1931, 59: 17--39

[4] He Y Z. On the algebroid functions and their derivatives(II). Acta Math Sinica, 1965, 15: 500--510

[5] He Y Z. Sur un problème d'unicité relatif aux fonctions algébroïdes. Sci Sinica, 1965, 14: 174--180

[6] He Y Z. On the multiple values of algebroid functions. Acta Math Sinica, 1979, 22: 733--742

[7] He Y Z, Gao S A. On algebroid functions taking the same values at the same points. Kodai Math J, 1986, 9: 256--265

[8] Gol'dberg A A, P'yana V A. Uniqueness theorems for rational, algabraic, and algebroid functions. Ukrainian Math J, 1994, 46: 219--235

[9] 孙道椿, 高宗升. 代数体函数的定理. 数学学报, 2006, 49: 1027--1032

[10] Xuan Z X, Gao Z S. Uniqueness theorems for algebroid functions. Complex Variables and Elliptic Equations, 2006, 51: 701--712

[11] 吕以辇, 张学莲. 黎曼曲面. 北京: 科学出版社, 1997

[12] 何育赞, 萧修治. 代数体函数与常微分方程. 北京: 科学出版社, 1988

[13] Selberg H. Über die wertverteilung der algebroiden funktionen. Math Z, 1930, 31: 709--729

[14] Ullrich E. Über den einfluss der verzwiegtheit einer algebroide auf ihre weitverteilung. J Reine Ang Math, 1931, 169: 198--220

[15] Gundersen G G. Meromorphic functions that share finite values with their derivative. J Math Anal Appl, 1980, 75: 441--446

[16] Mues E, Steinmetz N. Meromorphe funktionen, die mit ihrer ableitung werteteilen. Manuscripta Math, 1979, 29: 195--206