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

DOI:
https://doi.org/10.1090/S0002-9939-99-04789-9

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:
https://doi.org/10.1090/S0002-9939-99-04789-9

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