论文标题
复发序列中的代数度周期性
Algebraic Degree Periodicity in Recurrence Sequences
论文作者
论文摘要
代数线性复发序列中代数数的度序列实际上是周期性的。使用Skolem-Mahler-Lech定理证明了这一点。它具有在有限场上指数总和的程度序列和最小多项式序列的应用。程度周期性也适用于一些更复杂的非线性复发序列。我们从多项式图的迭代中给出了一个示例。这取决于在某些情况下已证明的动态Mordell-Lang猜想。
The degree sequence of the algebraic numbers in an algebraic linear recurrence sequence is shown to be virtually periodic. This is proved using the Skolem-Mahler-Lech theorem. It has applications to the degree sequence and the minimal polynomial sequence for exponential sums over finite fields. The degree periodicity also holds for some more complicated non-linear recurrence sequences. We give one example from the iterations of a polynomial map. This depending on the dynamic Mordell-Lang conjecture which has been proved in some cases.
