论文标题
使用Harvey的痕量公式计算代数曲线的Zeta函数
Computing zeta functions of algebraic curves using Harvey's trace formula
论文作者
论文摘要
我们提出了一种在有限场上计算代数曲线的Zeta功能的新方法。该算法依赖于Harvey的痕量公式来计算曲线平面模型上的点。然后，通过在单数点上进行校正来获得曲线的Zeta函数。我们报告了实施，并在岩浆中提供了一些示例，这些示例证明了对Tuitman算法的改进。
We present a new method for computing the zeta function of an algebraic curve over a finite field. The algorithm relies on a trace formula of Harvey to count points on a plane model of the curve. The zeta function of the curve is then obtained by making corrections at singular points. We report on an implementation and provide some examples in MAGMA which demonstrate an improvement over Tuitman's algorithm.
