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

Authors Cherry, W.
Yang, CC
Issue Date 1999
Source Proceedings of the American Mathematical Society , v. 127, (4), 1999, APR, p. 967-971
Summary 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.
Note First published in Proc. Amer. Math. Soc. in v. 127, no.4 (1999), published by the American Mathematical Society.
ISSN 0002-9939
Language English
Format Article
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