The Galois theory of the lemniscate
Amherst College Digital Collections > The Octagon
| Creator | Cox, David A. (Department of Mathematics and Statistics, Amherst College) |
|---|---|
| Creator | Hyde, Trevor (Department of Mathematics, University of Michigan) |
| Title | The Galois theory of the lemniscate |
| 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. |
| Notes | Published in print February 2014. |
| Journal Title | Journal of Number Theory |
| Publication Date | February 1, 2014 |
| Identifier (DOI) | 10.1016/j.jnt.2013.08.006 |
| Citation | Cox, David A., and Trevor Hyde. “The Galois Theory of the Lemniscate.” Journal of Number Theory 135 (2014): 43-59. |
| Languages | English |
| Genre | Article |
| Subject | Galois theory |
| Part of | The Amherst College Octagon |
| Repository | The Amherst College Octagon |
| Access and Use | Creative Commons Attribution-NonCommercial-NoDerivatives license (CC BY NC ND 4.0) |