Geodesic
On units of some fields of the form $\mathbb {Q}\big (\sqrt 2, \sqrt {p}, \sqrt {q}, \sqrt {-l}\big )$
Mathematica Bohemica, Tome 148 (2023) no. 2, pp. 237-242
Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

Let $p\equiv 1\pmod {8}$ and $q\equiv 3\pmod 8$ be two prime integers and let $\ell \not \in \{-1, p, q\}$ be a positive odd square-free integer. Assuming that the fundamental unit of $\mathbb {Q}\big (\sqrt {2p}\big ) $ has a negative norm, we investigate the unit group of the fields $\mathbb {Q}\big (\sqrt 2, \sqrt {p}, \sqrt {q}, \sqrt {-\ell } \big )$.
Let $p\equiv 1\pmod {8}$ and $q\equiv 3\pmod 8$ be two prime integers and let $\ell \not \in \{-1, p, q\}$ be a positive odd square-free integer. Assuming that the fundamental unit of $\mathbb {Q}\big (\sqrt {2p}\big ) $ has a negative norm, we investigate the unit group of the fields $\mathbb {Q}\big (\sqrt 2, \sqrt {p}, \sqrt {q}, \sqrt {-\ell } \big )$.
DOI : 10.21136/MB.2022.0128-21
Classification : 11R04, 11R27, 11R29, 11R37
Keywords: multiquadratic number field; unit group; fundamental system of units 
@article{10_21136_MB_2022_0128_21,
     author = {Chems-Eddin, Mohamed Mahmoud},
     title = {On units of some fields of the form $\mathbb {Q}\big (\sqrt 2, \sqrt {p}, \sqrt {q}, \sqrt {-l}\big )$},
     journal = {Mathematica Bohemica},
     pages = {237--242},
     year = {2023},
     volume = {148},
     number = {2},
     doi = {10.21136/MB.2022.0128-21},
     mrnumber = {4585579},
     zbl = {07729575},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0128-21/}
}
TY  - JOUR
AU  - Chems-Eddin, Mohamed Mahmoud
TI  - On units of some fields of the form $\mathbb {Q}\big (\sqrt 2, \sqrt {p}, \sqrt {q}, \sqrt {-l}\big )$
JO  - Mathematica Bohemica
PY  - 2023
SP  - 237
EP  - 242
VL  - 148
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0128-21/
DO  - 10.21136/MB.2022.0128-21
LA  - en
ID  - 10_21136_MB_2022_0128_21
ER  - 
%0 Journal Article
%A Chems-Eddin, Mohamed Mahmoud
%T On units of some fields of the form $\mathbb {Q}\big (\sqrt 2, \sqrt {p}, \sqrt {q}, \sqrt {-l}\big )$
%J Mathematica Bohemica
%D 2023
%P 237-242
%V 148
%N 2
%U http://geodesic.mathdoc.fr/articles/10.21136/MB.2022.0128-21/
%R 10.21136/MB.2022.0128-21
%G en
%F 10_21136_MB_2022_0128_21
Chems-Eddin, Mohamed Mahmoud. On units of some fields of the form $\mathbb {Q}\big (\sqrt 2, \sqrt {p}, \sqrt {q}, \sqrt {-l}\big )$. Mathematica Bohemica, Tome 148 (2023) no. 2, pp. 237-242. doi: 10.21136/MB.2022.0128-21

[1] Azizi, A.: Unités de certains corps de nombres imaginaires et abéliens sur $\mathbb{Q}$. Ann. Sci. Math. Qué. 23 (1999), 15-21 French. | MR | JFM

[2] Chems-Eddin, M. M.: Arithmetic of some real triquadratic fields: Units and 2-class groups. Available at , 32 pages. | arXiv

[3] Chems-Eddin, M. M.: Unit groups of some multiquadratic number fields and 2-class groups. Period. Math. Hung. 84 (2022), 235-249. | DOI | MR

[4] 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. | DOI | MR | JFM

[5] 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. | DOI | MR | JFM

[6] Kubota, T.: Über den bizyklischen biquadratischen Zahlkörper. Nagoya Math. J. 10 (1956), 65-85 German. | DOI | MR | JFM

[7] Varmon, J.: Über Abelsche Körper, deren alle Gruppeninvarianten aus einer Primzahl bestehen, und über Abelsche Körper als Kreiskörper. Hakan Ohlssons Boktryckeri, Lund (1925), German \99999JFM99999 51.0123.05.

[8] 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 \99999MR99999 0214565 . | MR | JFM

Cité par Sources :