Diagonal quadratic forms representing all binary diagonal quadratic forms

被引：0
|
作者：
Yun-Seong Ji
Myeong Jae Kim
Byeong-Kweon Oh
机构：
[1] Korea Advanced Institute of Science and Technology,Department of Mathematical Sciences
[2] Seoul National University,Department of Mathematical Sciences
[3] Seoul National University,Department of Mathematical Sciences and Research Institute of Mathematics
来源：
The Ramanujan Journal | 2018年 / 45卷
关键词：
Diagonal quadratic forms; Representations of binary quadratic forms; 2-universal quadratic forms; Primary 11E12; 11E20;
D O I：
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中图分类号：
学科分类号：
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.
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页码：21 / 32
页数：11
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