二元二次多项式的类数

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-06-04 DOI:10.1016/j.jnt.2025.04.012

Zichen Yang

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引用次数: 0

摘要

本文给出了在理想导体在二进位置上充分可除的条件下二元二次多项式的固有类数的一个公式。这使我们能够研究全正二元二次多项式的固有类数的增长。作为一个应用，我们证明了具有固定二次部分和固定固有类数的全正二元二次多项式的有限性结果。

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Class numbers of binary quadratic polynomials

In this paper, we give a formula for the proper class number of a binary quadratic polynomial assuming that the conductor ideal is sufficiently divisible at dyadic places. This allows us to study the growth of the proper class numbers of totally positive binary quadratic polynomials. As an application, we prove finiteness results on totally positive binary quadratic polynomials with a fixed quadratic part and a fixed proper class number.

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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.