## 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

## 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## References

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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: mayang@uxmail.ust.hk
- 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: https://doi.org/10.1090/S0002-9939-99-04789-9
- MathSciNet review: 1487362