论文标题
关于Skolem问题和一些有关线性复发序列的参数系列的相关问题
On the Skolem problem and some related questions for parametric families of linear recurrence sequences
论文作者
论文摘要
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 $ \ Mathbb Q $代数关闭的高度，Skolem问题是可以解决的，并且可以有效地确定此类序列中零的存在。我们还讨论了几个相关问题。
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.
