论文标题
在算术动力学中，在短时间间隔，雅各比多项式和单一政治家庭中完全真实的代数整数
Totally real algebraic integers in short intervals, Jacobi polynomials, and unicritical families in arithmetic dynamics
论文作者
论文摘要
我们将所有在最大的完全代数扩展为$ {\ Mathbb Q} $上定义的所有后有限的单次政治多项式分类。证明该结果的两个辅助结果可能具有一定的独立利益。第一个是间隔的$ n $直径的递归公式，该公式使用雅各比多项式的属性。第二个是一个数值标准，它允许一个人在任何代数整数的限制下，其所有复杂嵌入的实际间隔的长度小于$ 4 $。
We classify all post-critically finite unicritical polynomials defined over the maximal totally real algebraic extension of ${\mathbb Q}$. Two auxiliary results used in the proof of this result may be of some independent interest. The first is a recursion formula for the $n$-diameter of an interval, which uses properties of Jacobi polynomials. The second is a numerical criterion which allows one to the give a bound on the degree of any algebraic integer having all of its complex embeddings in a real interval of length less than $4$.
