Binomial Squares in Pure Cubic Number Fields
Number Theory
2011-10-10 v2
Abstract
Let K = Q(\omega) with \omega^3 = m be a pure cubic number field. We show that the elements\alpha \in K^\times whose squares have the form a - \omega form a group isomorphic to the group of rational points on the elliptic curve E_m: y^2= x^3 - m. We also show how to apply these results to the construction of unramified quadratic extensions of pure cubic number fields.
Cite
@article{arxiv.1108.6218,
title = {Binomial Squares in Pure Cubic Number Fields},
author = {Franz Lemmermeyer},
journal= {arXiv preprint arXiv:1108.6218},
year = {2011}
}