分离变量方程曲线上函数场点的高度
Heights of Function Field Points on Curves Given by Equations with Separated Variables
摘要：
设$P$和$Q$是特征为零的代数闭域$k$上的一元多项式.设$f$和$g$是$k$上的函数域$\K$的元素，使得$P(f)=Q(g).$，我们给出了关于$P$和$Q$，使得$f$和$g$的高度可以被有效地限制，而且，我们给出了关于$P$和$Q$的充分充分条件，其中$f$和$g$必须为常数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
