论文标题
在$ \ mathbb {q} $上定义的立方批判后有限多项式
Cubic post-critically finite polynomials defined over $\mathbb{Q}$
论文作者
论文摘要
我们描述并实施了一种算法，以查找在$ \ mathbb {q} $上定义的所有后有限的（PCF）立方多项式，最终可以超过$ \ text {pgl} _2 _2（\ bar {\ bar {\ mathbb {q}}）$。我们描述了正常形式，这些形式在尊重定义领域的同时对立方多项式的等效类别进行了分类。在$ \ mathbb {q} $的所有位置同时，将已知界限应用于这些正常形式的后界多项式的系数上，我们创建了可能是PCF的$ \ mathbb {q} $的有限搜索空间。使用计算机搜索这些可能是PCF立方多项式的搜索，我们发现15个实际上是PCF。
We describe and implement an algorithm to find all post-critically finite (PCF) cubic polynomials defined over $\mathbb{Q}$, up to conjugacy over $\text{PGL}_2(\bar{\mathbb{Q}})$. We describe normal forms that classify equivalence classes of cubic polynomials while respecting the field of definition. Applying known bounds on the coefficients of post-critically bounded polynomials to these normal forms simultaneously at all places of $\mathbb{Q}$, we create a finite search space of cubic polynomials over $\mathbb{Q}$ that may be PCF. Using a computer search of these possibly PCF cubic polynomials, we find fifteen which are in fact PCF.
