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

Jianing Li

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

Number Theory 2020-05-21 v1

Authors: Jianing Li

Abstract

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.

Keywords

2-adic logarithm fundamental unit quartic fields iwasawa modules coates-li conjecture

Cite

@article{arxiv.2005.09926,
  title  = {On the $2$-adic logarithm of units of certain totally imaginary quartic fields},
  author = {Jianing Li},
  journal= {arXiv preprint arXiv:2005.09926},
  year   = {2020}
}

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5 pages

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