Binomial squares in pure cubic number fields
نویسندگان
چکیده
Let K = Q(ω), with ω3 = m a positive integer, be a pure cubic number field. We show that the elements α ∈ K× whose squares have the form a − ω for rational numbers a form a group isomorphic to the group of rational points on the elliptic curve Em : y2 = x3 − m. This result will allow us to construct unramified quadratic extensions of pure cubic number fields K.
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