PreprintCC BY 4.0arXiv
On the unit group of some triquadratic fields
Abstract
In this paper, we calculate the unit groups and the $2$-class numbers of the fields $ \mathbb{Q}(\sqrt{2}, \sqrt{q}, \sqrt{rs})$, where q≡3pmod4, r and s are distinct prime numbers satisfying some congruent conditions. As an application of our main results, we derive the precise 2-class number for each field in our family. Furthermore, we show that Greenberg's conjecture is verified for several infinite families of real biquadratic fields.
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BibTeX
@misc{chemseddin2026unit,
title = {{On the unit group of some triquadratic fields}},
author = {Mohamed Mahmoud Chems-Eddin and Hamza El Mamry},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33110},
eprint = {2610.33110},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33110},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the unit group of some triquadratic fields
AU - Mohamed Mahmoud Chems-Eddin
AU - Hamza El Mamry
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.33110
UR - https://arxiv.org/abs/2610.33110
AB - In this paper, we calculate the unit groups and the $2$-class numbers of the fields $ \mathbb{Q}(\sqrt{2}, \sqrt{q}, \sqrt{rs})$, where q≡3pmod4, r and s are distinct prime numbers satisfying some congruent conditions. As an application of our main results, we derive the precise 2-class number for each field in our family. Furthermore, we show that Greenberg's conjecture is verified for several infinite families of real biquadratic fields.
ER -