On n-universal quadratic forms over dyadic local fields

被引：0

作者：

He, Zilong ^{[1
]}

Hu, Yong ^{[2
]}

机构：

[1] Dongguan Univ Technol, Sch Comp Sci & Technol, Dongguan 523808, Peoples R China

[2] Southern Univ Sci & Technol, Dept Math, Shenzhen 518055, Peoples R China

来源：

SCIENCE CHINA-MATHEMATICS | 2024年 / 67卷 / 07期

基金：

中国国家自然科学基金;

关键词：

integral quadratic forms; n-universal quadratic forms; dyadic fields; 290-theorem; LATTICES; NUMBER;

D O I：

10.1007/s11425-022-2133-0

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let n >= 2 be an integer. We give necessary and sufficient conditions for an integral quadratic form over dyadic local fields to be n-universal by using invariants from Beli's theory of bases of norm generators. Also, we provide a minimal set for testing n-universal quadratic forms over dyadic local fields, as an analogue of Bhargava and Hanke's 290-theorem (or Conway and Schneeberger's 15-theorem) on universal quadratic forms with integer coefficients.

引用

页码：1481 / 1506

页数：26

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