论文标题
从$ l $ functions中恢复对有限字段的仿射曲线
Recovering affine curves over finite fields from $L$-functions
论文作者
论文摘要
令$ k $为曲线的功能字段，在有限特征的有限字段上。我们使用$ k $的Galois扩展名的$ l $ functions进行调查，以有效地收回$ k $。当$ k $是删除四个合理点的投影线的功能字段时，我们将展示如何使用射线类字段的$ l $ functions，以有效地恢复投影线的自动形态的删除点。当$ k $是平面曲线的功能字段时，我们将展示如何使用$ k $的Artin-Schreier扩展名有效地恢复该曲线的方程。
Let $K$ be the function field of a curve over a finite field of odd characteristic. We investigate using $L$-functions of Galois extensions of $K$ to effectively recover $K$. When $K$ is the function field of the projective line with four rational points removed, we show how to use $L$-functions of a ray class field to effectively recover the removed points up to automorphisms of the projective line. When $K$ is the function field of a plane curve, we show how to effectively recover the equation of that curve using $L$-functions of Artin-Schreier extensions of $K$.
