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Uniqueness of non-Archimedean entire functions sharing sets of values counting multiplicity
Author(s):
William
Cherry;
Chung-Chun
Yang
Journal:
Proc. Amer. Math. Soc.
127
(1999),
967-971.
MSC (1991):
Primary 11S80, 30D35
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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:
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
Copyright of article:
Copyright
1999,
American Mathematical Society
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