论文标题
最小的普遍性标准设置在二次形式的表示形式上
Minimal universality criterion sets on the representations of quadratic forms
论文作者
论文摘要
对于具有有限等级的（正确定和积分）二次形式的集合$ s $，如果代表$ s $中的所有二次表格，则称为$ s $ f $，称为$ s $ umiversal。如果任何$ s_0 $ umiversal二次形式为$ s $ s $ umiversal，则子集$ s_0 $ $ s $称为$ s $ universality标准集。我们说，如果不存在$ s_0 $的适当子集，这是$ s $ $ s $ umiversality Criterion集合，则$ s_0 $是最小的。在本文中，我们研究了最小通用标准集的各种特性。特别是，我们表明，对于“大多数”二进制二进制形式$ f $，在$ s $是二进制形式$ f $的所有子形式的情况下，最小值$ s $ s $ umiversality标准集是唯一的。
For a set $S$ of (positive definite and integral) quadratic forms with bounded rank, a quadratic form $f$ is called $S$-universal if it represents all quadratic forms in $S$. A subset $S_0$ of $S$ is called an $S$-universality criterion set if any $S_0$-universal quadratic form is $S$-universal. We say $S_0$ is minimal if there does not exist a proper subset of $S_0$ that is an $S$-universality criterion set. In this article, we study various properties of minimal universality criterion sets. In particular, we show that for `most' binary quadratic forms $f$, minimal $S$-universality criterion sets are unique in the case when $S$ is the set of all subforms of the binary form $f$.
