数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (6): 1951-1965.

• 论文 • 上一篇    下一篇

HERMAN RINGS WITH SMALL PERIODS AND OMITTED VALUES

Tarun Kumar CHAKRA1, Gorachand CHAKRABORTY2, Tarakanta NAYAK1   

  1. 1 School of Basic Sciences, Indian Institute of Technology Bhubaneswar, India;
    2 Department of Mathematics, Goverment General Degree College, Manbazar Ⅱ, Purulia, India
  • 收稿日期:2017-03-06 修回日期:2018-05-21 出版日期:2018-12-25 发布日期:2018-12-28
  • 通讯作者: Tarun Kumar CHAKRA E-mail:tkc10@iitbbs.ac.in
  • 作者简介:Gorachand CHAKRABORTY,E-mail:gorachand11@gmail.com;Tarakanta NAYAK,E-mail:tnayak@iitbbs.ac.cn
  • 基金资助:
    The first and third authors are supported by CSIR and Department of Science and Technology, Goverment of India through a Fast Track Project (SR-FTP-MS019-2011) respectively.

HERMAN RINGS WITH SMALL PERIODS AND OMITTED VALUES

Tarun Kumar CHAKRA1, Gorachand CHAKRABORTY2, Tarakanta NAYAK1   

  1. 1 School of Basic Sciences, Indian Institute of Technology Bhubaneswar, India;
    2 Department of Mathematics, Goverment General Degree College, Manbazar Ⅱ, Purulia, India
  • Received:2017-03-06 Revised:2018-05-21 Online:2018-12-25 Published:2018-12-28
  • Contact: Tarun Kumar CHAKRA E-mail:tkc10@iitbbs.ac.in
  • Supported by:
    The first and third authors are supported by CSIR and Department of Science and Technology, Goverment of India through a Fast Track Project (SR-FTP-MS019-2011) respectively.

摘要: All possible arrangements of cycles of three periodic as well as four periodic Herman rings of transcendental meromorphic functions having at least one omitted value are determined. It is shown that if p=3 or 4, then the number of p-cycles of Herman rings is at most one. We have also proved a result about the non-existence of a 3-cycle and a 4-cycle of Herman rings simultaneously. Finally some examples of functions having no Herman ring are discussed.

关键词: omitted values, Herman rings and transcendental meromorphic functions

Abstract: All possible arrangements of cycles of three periodic as well as four periodic Herman rings of transcendental meromorphic functions having at least one omitted value are determined. It is shown that if p=3 or 4, then the number of p-cycles of Herman rings is at most one. We have also proved a result about the non-existence of a 3-cycle and a 4-cycle of Herman rings simultaneously. Finally some examples of functions having no Herman ring are discussed.

Key words: omitted values, Herman rings and transcendental meromorphic functions