Composition of binary quadratic forms over number fields

被引：1

作者：

Zemkova, Kristyna ^{[1
,2
]}

机构：

[1] Charles Univ Prague, Fac Math & Phys, Dept Algebra, Sokolovska 83, Prague 18600 8, Czech Republic

[2] Tech Univ Dortmund, Fak Math, D-44221 Dortmund, Germany

来源：

MATHEMATICA SLOVACA | 2021年 / 71卷 / 06期

关键词：

binary quadratic forms; Gauss composition; class group; GAUSS COMPOSITION;

D O I：

10.1515/ms-2021-0057

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, the standard correspondence between the ideal class group of a quadratic number field and the equivalence classes of binary quadratic forms of given discriminant is generalized to any base number field of narrow class number one. The article contains an explicit description of the correspondence. In the case of totally negative discriminants, equivalent conditions are given for a binary quadratic form to be totally positive definite.

引用

页码：1339 / 1360

页数：22

共 50 条

[21] Binary trilinear forms and the composition of binary quadratic forms.
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[22] INDECOMPOSABLE HERMITIAN FORMS OVER QUADRATIC NUMBER FIELDS - PRELIMINARY REPORT
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