Acta mathematica scientia,Series B ›› 2018, Vol. 38 ›› Issue (6): 1951-1965.

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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.

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

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