Abstract
Let K be a complete ultrametric algebraically closed field, let A ( K) be the ring of entire functions in K. Unique Range Sets ( urs's) were defined in [5], and studied in [6] for complex entire or meromorphic functions. Here, we characterize the urs's for polynomials, in any algebraically closed field, and we prove that in non archimedean analysis, there exist urs's of n elements, for entire functions, for any n ≥ 3. When n = 3, we can characterize the sets of three elements that are urs's for entire functions.
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