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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Uniqueness of non-Archimedean entire functions sharing sets of values counting multiplicity


Authors: William Cherry and Chung-Chun Yang
Journal: Proc. Amer. Math. Soc. 127 (1999), 967-971
MSC (1991): Primary 11S80, 30D35
MathSciNet review: 1487362
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Abstract: 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

Chung-Chun Yang
Affiliation: Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong
Email: mayang@uxmail.ust.hk

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04789-9
PII: S 0002-9939(99)04789-9
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
Article copyright: © Copyright 1999 American Mathematical Society