Binomial squares in pure cubic number fields

被引：2
作者：
Lemmermeyer, Franz
机构：
[1] not available, 73489 Jagstzell
来源：
JOURNAL DE THEORIE DES NOMBRES DE BORDEAUX | 2012年 / 24卷 / 03期
关键词：
D O I：
10.5802/jtnb.817
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let .K = Q(omega), with omega(3) = m a positive integer, be a pure cubic number field. We show that the elements alpha is an element of K-x whose squares have the form a - omega for rational numbers a form a group isomorphic to the group of rational points on the elliptic curve E-m : y(2) = x(3) - m. This result will allow us to construct unramified quadratic extensions of pure cubic number fields K.
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页码：691 / 704
页数：14
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