数学物理学报 ›› 2013, Vol. 33 ›› Issue (5): 819-828.

• 论文 • 上一篇    下一篇

亚纯函数f(qz+c)}的Nevanlinna 理论以及应用的研究

祁晓光1|刘永2|杨连中2   

  1. 1.济南大学 数学科学学院 济南 250022;
    2.山东大学 数学学院 济南 250100
  • 收稿日期:2012-03-07 修回日期:2013-05-27 出版日期:2013-10-25 发布日期:2013-10-25
  • 基金资助:

    数学天元基金(11226094)、山东省自然科学基金(ZR2012AQ020, ZR2010AM030)和济南大学博士基金(XBS1211)资助.

Nevanlinna Theory for the f(qz+c) and Its Applications

 QI Xiao-Guang1, LIU Yong2, YANG Lian-Zhong2   

  1. 1.University of Jinan, School of Mathematics, Jinan |250022|2.Shandong University, School of Mathematics, Jinan |250100
  • Received:2012-03-07 Revised:2013-05-27 Online:2013-10-25 Published:2013-10-25
  • Supported by:

    数学天元基金(11226094)、山东省自然科学基金(ZR2012AQ020, ZR2010AM030)和济南大学博士基金(XBS1211)资助.

摘要:

通过研究f(qz+c)/f(z)的均值函数, 得到Nevanlinna 理论第二基本定理的q 阶差分对应. 作为应用,给出了T(r, f(qz+c)) 与T(r, f) 之间的关系, 并考虑了函数f(z)与f(qz+c) 的分担值问题.

关键词: 亚纯函数, Nevanlinna 理论, 分担值

Abstract:

In this paper, we investigate the proximity function of f(qz+c)/f(z) and present a q-shift difference analogue of the second main theorem of Nevanlinna theory. As applications, we will give the relation of T(r, f(qz+c)) and T(r, f), and consider the value sharing problem of f(z) and its q-shift difference f(qz+c) as well.

Key words: Meromorphic functions, Nevanlinna theory, Sharing value

中图分类号: 

  • 30D35