Abstract
Let F be the completion, with respect to the degree valuation, of the field of rational functions over , the Galois (finite) field of q elements. A function f : F → F is integer-valued if . An integer-valued function f is called a pseudo-polynomial iff(M+K)≡f(M)(modK)for all and . Based on an interpolation series introduced by Carlitzin 1935, explicit shapes of pseudo-polynomials are established. Using an asymptotic characterization of polynomials, it is also proved that the set of all pseudo-polynomials is an integral domain but not a unique factorization domain.
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