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Equations in the Hadamard ring of rational functions

Andrea Ferretti; Umberto Zannier — 2007

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

Let $K$ be a number field. It is well known that the set of recurrencesequences with entries in $K$ is closed under component-wise operations, and so it can be equipped with a ring structure. We try to understand the structure of this ring, in particular to understand which algebraic equations have a solution in the ring. For the case of cyclic equations a conjecture due to Pisot states the following: assume ${a_{n}}$ is a recurrence sequence and suppose that all the $a_{n}$ have a $d^{th}$ root in the field $K$ ; then (after...

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