A NOTE ON THE MINIMAL INDICES OF PURE CUBIC FIELDS

被引：0

作者：

Gaal, Istvan ^{[1
]}

Szabo, Timea ^{[1
]}

机构：

[1] Univ Debrecen, Math Inst, Pf 12, H-4010 Debrecen, Hungary

来源：

JP JOURNAL OF ALGEBRA NUMBER THEORY AND APPLICATIONS | 2010年 / 19卷 / 02期

关键词：

pure cubic fields; power integral bases; minimal indices;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Using standard techniques, we study the existence of power integral bases and the behaviour of minimal indices of pure cubic fields of type K = Q(3 root n) up to discriminant vertical bar D vertical bar < 3 .10(6) and vertical bar D vertical bar < 12 .10(6), respectively. Such calculations for these special fields are performed here for the first time. This yields to solve cubic Thue equations, that may have extreme coefficients in some examples. Based on our computational results on index form equations in these fields, we consider the frequency of fields with power integral bases and the average behaviour of minimal indices.

引用

页码：129 / 139

页数：11