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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Herman rings of meromorphic maps with an omitted value
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by Tarakanta Nayak PDF
Proc. Amer. Math. Soc. 144 (2016), 587-597 Request permission


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
  • MR Author ID: 806609
  • Email:
  • 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
  • © Copyright 2015 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 144 (2016), 587-597
  • MSC (2010): Primary 37F10; Secondary 32A20
  • DOI:
  • MathSciNet review: 3430836