Asian Journal of Mathematics

Volume 25 (2021)

Number 2

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

Pages: 177 – 182



Jianing Li (Research Center for Mathematics and Interdisciplinary Sciences, Shandong University, Qingdao, China)


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


$2$‑adic logarithm, units, class groups, pure quartic fields

2010 Mathematics Subject Classification

11R27, 11R29

The author is supported by the Fundamental Research Funds for the Central Universities (No. WK3470000020) and by the Anhui Initiative in Quantum Information Technologies (Grant No. AHY150200)

Received 5 April 2020

Accepted 11 June 2020

Published 15 October 2021