关于参数线性递归序列族的Skolem问题及有关问题
On the Skolem problem and some related questions for parametric families of linear recurrence sequences
摘要：
我们证明了在一个参数族的线性递归序列$a_1(α) f_1(α)^n + \ldots + a_k(α) f_k(α)^n$与系数$a_i$和特征根$f_i$，$i=1, \ldots,k$，由有理函数在某些数域上，对于所有，但一组$α$的有界高度的代数闭包$\mathbb Q$，Skolem问题是可解的，并在这样的序列中的零的存在性，可以有效地确定。我们还讨论了几个相关的问题。
英文摘要：
We show that in a parametric family of linear recurrence sequences $a_1(α) f_1(α)^n + \ldots + a_k(α) f_k(α)^n$ 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 $α$ 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.
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