论文标题
由具有分离变量的方程式给出的曲线上功能场点的高度
Heights of Function Field Points on Curves Given by Equations with Separated Variables
论文作者
论文摘要
让$ p $和$ q $是一个变量的多项式，在代数封闭的特征零的$ k $上。让$ f $和$ g $是$ k $上的功能字段$ \ k $的元素，这样$ p（f）= q（g）。$我们给出$ p $和$ q $的条件，这样，$ f $ and $ g $的高度有效地限制了，而且我们可以在$ p $和$ q $ f $ g $和$ g $的情况下提供足够的条件。
Let $P$ and $Q$ be polynomials in one variable over an algebraically closed field $k$ of characteristic zero. Let $f$ and $g$ be elements of a function field $\K$ over $k$ such that $P(f)=Q(g).$ We give conditions on $P$ and $Q$ such that the height of $f$ and $g$ can be effectively bounded, and moreover, we give sufficient conditions on $P$ and $Q$ under which $f$ and $g$ must be constant.
