Binomial Squares in Pure Cubic Number Fields

Details Binomial Squares in Pure Cubic Number Fields Binomial Squares in Pure Cubic Number Fields

2011-08-31

arxiv.org/abs/1108.6218v2

Mathematics

Number Theory

Scientific paper

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.

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