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A note on the Hadamard $$k$$th root of a rational function. (English) Zbl 0635.10008
A generalization of a conjecture of Pisot asserts that the Hadamard $$k$$th root of a rational function $$f$$ whose Taylor coefficients are $$k$$th powers of elements belonging to some finitely generated extension field $$F$$ of $$\mathbb Q$$ is a rational function. The authors show that it is sufficient to prove the conjecture in the case that $$F$$ is a number field, and prove the conjecture under the assumption that $$f$$ has a dominant pole.

##### MSC:
 11B37 Recurrences