Geometry of biquadratic and cyclic cubic log-unit lattices

JOURNAL OF NUMBER THEORY

卷:228

Article

Tellez, Fernando Azpeitia¹  Powell, Christopher²  Sharif, Shahed¹ 

[1] Calif State Univ San Marcos, San Marcos, TX 92096 USA

[2] BAE Syst Inc, Arlington, TX USA

关键词: Units in number fields;    Lattices;    Log embedding;   

DOI  :  10.1016/j.jnt.2021.04.007

来源: Elsevier

【 摘 要 】

By Dirichlet's Unit Theorem, under the log embedding the units in the ring of integers of a number field form a lattice, called the log-unit lattice. We investigate the geometry of these lattices when the number field is a biquadratic or cyclic cubic extension of Q. In the biquadratic case, we determine when the log-unit lattice is orthogonal. In the cyclic cubic case, we show that the log-unit lattice is always equilateral triangular. (c) 2021 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

【 授权许可】

Free