Linear recurrence relations for some generalized Pisot sequences. (English) Zbl 0790.11012

Gouvêa, Fernando Q. (ed.) et al., Advances in number theory. The proceedings of the third conference of the Canadian Number Theory Association, held at Queen’s University, Kingston, Canada, August 18-24, 1991. Oxford: Clarendon Press. 333-340 (1993).
For a given real number \(r\) and integers \(0< a_ 0<a_ 1\) one defines the sequence \(E_ r(a_ 0,a_ 1)\) by putting \(a_{n+2}=\bigl[a^ 2_{n+1}/a_ n+ r\bigr]\). The author deals with the question when such a sequence satisfies a linear recurrence relation and obtains in the cases \(r=0\) and \(r=1\) restrictions for the minimal polynomials of such recurrences.
For the entire collection see [Zbl 0773.00021].


11B37 Recurrences
11R06 PV-numbers and generalizations; other special algebraic numbers; Mahler measure