具有规定判别和伽罗瓦闭群的野生四分群计数

IF 0.6 3区 数学 Q3 MATHEMATICS
Sebastian Monnet
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引用次数: 0

摘要

给定一个二进域K,在给定判别值和伽罗瓦闭包群的情况下,给出了完全分枝的四进域扩展L/K的个数。我们用这些公式证明了Serre质量公式的改进,它将应用于数域的算术统计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Counting wild quartics with prescribed discriminant and Galois closure group
Given a 2-adic field K, we give a formula for the number of totally ramified quartic field extensions L/K with a given discriminant valuation and Galois closure group. We use these formulae to prove refinements of Serre's mass formula, which will have applications to the arithmetic statistics of number fields.
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来源期刊
Journal of Number Theory
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.
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