Diagonal quadratic forms representing all binary diagonal quadratic forms

被引：1

作者：

Ji, Yun-Seong ^{[1
]}

Kim, Myeong Jae ^{[2
]}

Oh, Byeong-Kweon ^{[2
,3
]}

机构：

[1] Korea Adv Inst Sci & Technol, Dept Math Sci, Daejeon 305701, South Korea

[2] Seoul Natl Univ, Dept Math Sci, Seoul 151747, South Korea

[3] Seoul Natl Univ, Res Inst Math, Seoul 151747, South Korea

来源：

RAMANUJAN JOURNAL | 2018年 / 45卷 / 01期

基金：

新加坡国家研究基金会;

关键词：

Diagonal quadratic forms; Representations of binary quadratic forms; 2-universal quadratic forms; ODD POSITIVE INTEGERS; UNIVERSAL FORMS; RANK;

D O I：

10.1007/s11139-016-9857-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A (positive definite integral) quadratic form is called diagonally 2-universal if it represents all positive definite integral binary diagonal quadratic forms. In this article, we show that, up to equivalence, there are exactly 18 (positive definite integral) quinary diagonal quadratic forms that are diagonally 2-universal. Furthermore, we provide a "diagonally 2-universal criterion" for diagonal quadratic forms, which is similar to "15-Theorem" proved by Conway and Schneeberger.

引用

页码：21 / 32

页数：12