双纽线的伽罗瓦论
The Galois theory of the lemniscate
摘要：
本文研究双纽线的分界点所产生的伽罗瓦群。我们以两种方式计算这些伽罗瓦群：第一，通过类域，第二，通过证明引理多项式的不可约性，引理多项式是分圆多项式的类似物。我们还讨论了双纽线上的Abel定理，并解释了双纽线多项式与切比雪夫多项式的关系。
英文摘要：
This article studies the Galois groups that arise from division points of the lemniscate. We compute these Galois groups two ways: first, by class field theory, and second, by proving the irreducibility of lemnatomic polynomials, which are analogs of cyclotomic polynomials. We also discuss Abel's theorem on the lemniscate and explain how lemnatomic polynomials relate to Chebyshev polynomials.
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。
