论文标题
部分可观测时空混沌系统的无模型预测
Primality proving using elliptic curves with complex multiplication by imaginary quadratic fields of class number three
论文作者
论文摘要
2015年，Abatzoglou，Silverberg，Sutherland和Wong提出了使用具有复杂乘法的椭圆形曲线的特殊整数序列的原始算法的框架。他们应用了框架来获得椭圆形曲线的算法，该算法通过第一和第二类假想的二次乘以复杂的乘法，但是，在较高的类数字的情况下，他们无法获得原始算法证明算法。在本文中，我们提出了一种将其框架应用于第三类假想的二次字段的方法。特别是，我们的方法通过使用类似的第三类假想的二次二次字段，在其中2个分开的类别的二次字段提供了比现有算法的特殊序列更有效的原始算法。作为一个应用程序，我们提供了两个特殊的整数序列，这些整数序列衍生自$ \ q（\ sqrt {-23}）$和$ \ q（\ sqrt {-31}）$，它们是类数字的所有想象中的Quadratic字段，其中三个中的第三个中的三个分数。最后，我们给出了这些序列的原则的计算结果。
In 2015, Abatzoglou, Silverberg, Sutherland, and Wong presented a framework for primality proving algorithms for special sequences of integers using an elliptic curve with complex multiplication. They applied their framework to obtain algorithms for elliptic curves with complex multiplication by imaginary quadratic field of class numbers one and two, but, they were not able to obtain primality proving algorithms in cases of higher class number. In this paper, we present a method to apply their framework to imaginary quadratic fields of class number three. In particular, our method provides a more efficient primality proving algorithm for special sequences of integers than the existing algorithms by using an imaginary quadratic field of class number three in which 2 splits. As an application, we give two special sequences of integers derived from $\Q(\sqrt{-23})$ and $\Q(\sqrt{-31})$, which are all the imaginary quadratic fields of class number three in which 2 splits. Finally, we give a computational result for the primality of these sequences.
