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Herman rings of meromorphic maps with an omitted value


Author: Tarakanta Nayak
Journal: Proc. Amer. Math. Soc. 144 (2016), 587-597
MSC (2010): Primary 37F10; Secondary 32A20
DOI: https://doi.org/10.1090/proc12715
Published electronically: August 20, 2015
MathSciNet review: 3430836
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Abstract: We investigate the existence and distribution of Herman rings of transcendental meromorphic functions which have at least one omitted value. If all the poles of such a function are multiple, then it has no Herman ring. Herman rings of period one or two do not exist. Functions with a single pole or with at least two poles, one of which is an omitted value, have no Herman ring. Every doubly connected periodic Fatou component is a Herman ring.


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Additional Information

Tarakanta Nayak
Affiliation: School of Basic Sciences, Indian Institute of Technology, Bhubaneswar, India
Email: tnayak@iitbbs.ac.in

DOI: https://doi.org/10.1090/proc12715
Keywords: Herman ring, omitted value, meromorphic function
Received by editor(s): November 3, 2012
Received by editor(s) in revised form: May 23, 2014, and December 30, 2014
Published electronically: August 20, 2015
Additional Notes: The author was supported by the Department of Science & Technology, Govt. of India through the Fast Track Project (SR/FTP/MS-019/2011).
Communicated by: Nimish Shah
Article copyright: © Copyright 2015 American Mathematical Society