双纽线的伽罗瓦理论
数论
2012-08-22 v2
摘要
本文研究了由双纽线分割点产生的伽罗瓦群。我们通过两种方式计算这些伽罗瓦群：首先利用类域论，其次通过证明双纽原子多项式（lemnatomic polynomials，即分圆多项式的类比）的不可约性。我们还讨论了关于双纽线的阿贝尔定理，并解释了双纽原子多项式与切比雪夫多项式之间的关系。
引用
@article{arxiv.1208.2653,
title = {The Galois theory of the lemniscate},
author = {David A. Cox and Trevor Hyde},
journal= {arXiv preprint arXiv:1208.2653},
year = {2012}
}
备注
The revised version adds four references and some historical remarks. We also note that a special case of Theorem 4.1 appears in Lemmermeyer's Reciprocity Laws