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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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Uniqueness of non-Archimedean entire functions sharing sets of values counting multiplicity
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by William Cherry and Chung-Chun Yang PDF
Proc. Amer. Math. Soc. 127 (1999), 967-971 Request permission


A set is called a unique range set for a certain class of functions if each inverse image of that set uniquely determines a function from the given class. We show that a finite set is a unique range set, counting multiplicity, for non-Archimedean entire functions if and only if there is no non-trivial affine transformation preserving the set. Our proof uses a theorem of Berkovich to extend, to non-Archimedean entire functions, an argument used by Boutabaa, Escassut, and Haddad to prove this result for polynomials
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Additional Information
  • William Cherry
  • Affiliation: School of Mathematics, Institute for Advanced Study, Princeton, New Jersey 08540
  • Address at time of publication: Department of Mathematics, University of North Texas, Denton, Texas 76203
  • MR Author ID: 292846
  • Chung-Chun Yang
  • Affiliation: Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
  • Email:
  • Received by editor(s): July 18, 1997
  • Additional Notes: Financial support for the first author was provided by National Science Foundation grants DMS-9505041 and DMS-9304580
    The second author’s research was partially supported by a UGC grant of Hong Kong.
  • Communicated by: David E. Rohrlich
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 967-971
  • MSC (1991): Primary 11S80, 30D35
  • DOI:
  • MathSciNet review: 1487362