ON THE RANK OF UNIVERSAL QUADRATIC FORMS OVER REAL QUADRATIC FIELDS

被引：0

作者：

Blomer, Valentin ^{[1
]}

Kala, Vitezslav ^{[1
,2
]}

机构：

[1] Univ Gottingen, Math Inst, Bunsenstr 3-5, D-37073 Gottingen, Germany

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

来源：

DOCUMENTA MATHEMATICA | 2018年 / 23卷

关键词：

universal quadratic form; real quadratic number field; continued fraction; additively indecomposable integer;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the minimal number of variables required by a totally positive definite diagonal universal quadratic form over a real quadratic field Q(root D) and obtain lower and upper bounds for it in terms of certain sums of coefficients of the associated continued fraction. We also estimate such sums in terms of D and establish a link between continued fraction expansions and special values of L-functions in the spirit of Kronecker's limit formula.

引用

页码：15 / 34

页数：20

共 30 条

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