Universal quadratic forms and indecomposables over biquadratic fields

被引：13

作者：

Cech, Martin ^{[1
]}

Lachman, Dominik ^{[1
]}

Svoboda, Josef ^{[1
]}

Tinkova, Magdalena ^{[1
]}

Zemkova, Kristysma ^{[1
]}

机构：

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

来源：

MATHEMATISCHE NACHRICHTEN | 2019年 / 292卷 / 03期

关键词：

biquadratic number field; indecomposable integer; universal quadratic form; INTEGERS;

D O I：

10.1002/mana.201800109

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this article is to study (additively) indecomposable algebraic integers O-K of biquadratic number fields K and universal totally positive quadratic forms with coefficients in O-K. There are given sufficient conditions for an indecomposable element of a quadratic subfield to remain indecomposable in the biquadratic number field K. Furthermore, estimates are proven which enable algorithmization of the method of escalation over K. These are used to prove, over two particular biquadratic number fields Q(root 2, root 3) and Q(root 6, root 19), a lower bound on the number of variables of a universal quadratic forms.

引用

页码：540 / 555

页数：16

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