The Galois theory of the lemniscate
Number Theory
2012-08-22 v2
Abstract
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.
Keywords
Cite
@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}
}
Comments
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