某些全虚四次域单位的$2$进对数

IF 0.5 4区数学 Q3 MATHEMATICS

Asian Journal of Mathematics Pub Date : 2020-05-20 DOI:10.4310/ajm.2021.v25.n2.a1

Jianing Li

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引用次数: 4

摘要

本文证明了域$\mathbb{Q}(\sqrt[4]{-q}) $的基本单位的$2$ -进对数的一个结果，其中$q\equiv 3\bmod 4$是素数。当$q\equiv 15\bmod 16$，这一结果证实了coats - li的推测，并对他们工作中出现的某些Iwasawa模块产生了影响。

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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On the $2$-adic logarithm of units of certain totally imaginary quartic fields

In this paper, we prove a result on the $2$-adic logarithm of the fundamental unit of the field $\mathbb{Q}(\sqrt[4]{-q}) $, where $q\equiv 3\bmod 4$ is a prime. When $q\equiv 15\bmod 16$, this result confirms a speculation of Coates-Li and has consequences for certain Iwasawa modules arising in their work.

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