原始二全积分二次型

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory 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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.