×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite