有限代数数环及其在素数分解定律中的应用

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2024-05-24 DOI:10.1016/j.jnt.2024.04.003

Julian Rosen , Yoshihiro Takeyama , Koji Tasaka , Shuji Yamamoto

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引用次数: 0

摘要

在本文中，我们开发了一种用线性循环序列表达有限代数数（特别是其中某些幂级数）的明确方法，并将其应用于有理域上给定有限伽罗瓦扩展中分裂素数的表征。

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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The ring of finite algebraic numbers and its application to the law of decomposition of primes

In this paper, we develop an explicit method to express finite algebraic numbers (in particular, certain idempotents among them) in terms of linear recurrent sequences, and give applications to the characterization of the splitting primes in a given finite Galois extension over the rational field.

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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.