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Mathematics, Number Theory
Abstract:
We show that in a parametric family of linear recurrence sequences
$a_1(\alpha) f_1(\alpha)^n + \ldots + a_k(\alpha) f_k(\alpha)^n$ with the
coefficients $a_i$ and characteristic roots $f_i$, $i=1, \ldots,k$, given by
rational functions over some number field, for all but a set of $\alpha$ of
bounded height in the algebraic closure of $\mathbb Q$, the Skolem problem is
solvable, and the existence of a zero in such a sequence can be effectively
decided. We also discuss several related questions.
