原始二全积分二次型

Pub Date : 2024-06-25 DOI:10.1016/j.jnt.2024.05.006

Byeong-Kweon Oh , Jongheun Yoon

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引用次数: 0

摘要

对于一个正整数，如果一个（正定积分）二次型原始地代表了所有秩的二次型，那么这个二次型就叫做原始通用二次型。有学者证明，基元 1-Universal 四元二次函数形式的等价类恰好有 107 个。在本文中，我们将证明 primitively 2-universal quadratic forms 的最小秩是 6，并且正好有 201 个 primitively 2-universal senary quadratic forms 的等价类。

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Primitively 2-universal senary integral quadratic forms

For a positive integer m, a (positive definite integral) quadratic form is called primitively m-universal if it primitively represents all quadratic forms of rank m. It was proved in [9] that there are exactly 107 equivalence classes of primitively 1-universal quaternary quadratic forms. In this article, we prove that the minimal rank of primitively 2-universal quadratic forms is six, and there are exactly 201 equivalence classes of primitively 2-universal senary quadratic forms.

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