| Title:
|
The unit group of some fields of the form $\mathbb {Q}(\sqrt {2}, \sqrt {p}, \sqrt {q}, \sqrt {-l})$ (English) |
| Author:
|
El Hamam, Moha Ben Taleb |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
149 |
| Issue:
|
1 |
| Year:
|
2024 |
| Pages:
|
49-55 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $p$ and $q$ be two different prime integers such that $p\equiv q\equiv 3\pmod 8$ with $(p/q)=1$, and $l$ a positive odd square-free integer relatively prime to $p$ and $q$. In this paper we investigate the unit groups of number fields $\mathbb L=\mathbb {Q}(\sqrt {2}, \sqrt {p}, \sqrt {q}, \sqrt {-l})$. (English) |
| Keyword:
|
unit group |
| Keyword:
|
multiquadratic number fields |
| Keyword:
|
unit index |
| MSC:
|
11R04 |
| MSC:
|
11R27 |
| MSC:
|
11R29 |
| idZBL:
|
Zbl 07830543 |
| idMR:
|
MR4715556 |
| DOI:
|
10.21136/MB.2023.0077-22 |
| . |
| Date available:
|
2024-03-13T10:18:12Z |
| Last updated:
|
2024-12-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152292 |
| . |
| Reference:
|
[1] Azizi, A.: Unités de certains corps de nombres imaginaires et abéliens sur $\Bbb Q$.Ann. Sci. Math. Qué. 23 (1999), 15-21 French \99999MR99999 1721726 . Zbl 1041.11072, MR 1721726 |
| Reference:
|
[2] Azizi, A., Chems-Eddin, M. M., Zekhnini, A.: Note on the Hilbert 2-class field tower.Math. Bohem. 147 (2022), 513-524 \99999DOI99999 10.21136/MB.2022.0056-21 . MR 4512171 |
| Reference:
|
[3] Chems-Eddin, M. M.: Arithmetic of some real triquadratic fields: Units and 2-class groups.Available at https://arxiv.org/abs/2108.04171v1 (2021), 32 pages. |
| Reference:
|
[4] Chems-Eddin, M. M.: Unit groups of some multiquadratic number fields and 2-class groups.Period. Math. Hung. 84 (2022), 235-249. Zbl 07551296, MR 4423478, 10.1007/s10998-021-00402-0 |
| Reference:
|
[5] Chems-Eddin, M. M.: On units of some fields of the form $\Bbb{Q}(\sqrt2, \sqrt{p}, \sqrt{q}, \sqrt{-\ell})$.Math. Bohem. 148 (2023), 237-242. Zbl 7729575, MR 4585579, 10.21136/MB.2022.0128-21 |
| Reference:
|
[6] Chems-Eddin, M. M., Azizi, A., Zekhnini, A.: Unit groups and Iwasawa lambda invariants of some multiquadratic number fields.Bol. Soc. Mat. Mex, III. Ser. 27 (2021), Article ID 24, 16 pages. Zbl 1468.11223, MR 4220815, 10.1007/s40590-021-00329-z |
| Reference:
|
[7] Chems-Eddin, M. M., Zekhnini, A., Azizi, A.: Units and 2-class field towers of some multiquadratic number fields.Turk. J. Math. 44 (2020), 1466-1483. Zbl 1455.11140, MR 4122918, 10.3906/mat-2003-117 |
| Reference:
|
[8] Chems-Eddin, M. M., Zekhnini, A., Azizi, A.: On the Hilbert 2-class field towers of some cyclotomic $\Bbb Z_2$-extensions.Available at https://arxiv.org/abs/2005.06646 (2021), 15 pages. MR 4769739 |
| Reference:
|
[9] Chems-Eddin, M. M., Zekhnini, A., Azizi, A.: Unit groups of some multiquadratic number fields of degree 16.São Paulo J. Math. Sci 16 (2022), 1091-1096. Zbl 7626140, MR 4515950, 10.1007/s40863-020-00209-w |
| Reference:
|
[10] Kubota, T.: Über den bizyklischen biquadratischen Zahlkörper.Nagoya Math. J. 10 (1956), 65-85 German. Zbl 0074.03001, MR 0083009, 10.1017/S0027763000000088 |
| Reference:
|
[11] Wada, H.: On the class number and the unit group of certain algebraic number fields.J. Fac. Sci., Univ. Tokyo, Sect. I 13 (1966), 201-209. Zbl 0158.30103, MR 0214565 |
| . |
