The Galois theory of the lemniscate

JOURNAL OF NUMBER THEORY

卷:135

Article

Cox, David A.¹  Hyde, Trevor² 

[1] Amherst Coll, Dept Math, Amherst, MA 01002 USA

[2] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

关键词: Lemniscate;    Galois group;    Chebyshev polynomial;   

DOI  :  10.1016/j.jnt.2013.08.006

来源: Elsevier

【 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. (C) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free