| Title:
|
The non-normal quartic CM-fields and the dihedral octic CM-fields with ideal class groups of exponent $\le 2$ (English) |
| Author:
|
Louboutin, Stéphane |
| Author:
|
Yang, Hee-Sun |
| Author:
|
Kwon, Soun-Hi |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
54 |
| Issue:
|
5 |
| Year:
|
2004 |
| Pages:
|
535-574 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11R29 |
| MSC:
|
11R37 |
| MSC:
|
11Y40 |
| idZBL:
|
Zbl 1108.11085 |
| idMR:
|
MR2114623 |
| . |
| Date available:
|
2009-09-25T14:23:47Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133206 |
| . |
| Reference:
|
[Ear] EARNEST A. G.: Exponents of the class groups of imaginary abelian number fields.Bull. Austral. Math. Soc. 35 (1987), 231-245. Zbl 0597.12006, MR 0878434 |
| Reference:
|
[Lan1] LANG S.: Cyclotomic Fields I and II.(combined 2nd ed.). Grad. Texts in Math. 121, Springer-Verlag, New York, 1990. Zbl 0704.11038, MR 1029028 |
| Reference:
|
[Lan2] LANG S.: Algebraic Number Theory.(2nd ed.). Grad. Texts in Math. 110, Springer-Verlag, New York, 1994. Zbl 0811.11001, MR 1282723 |
| Reference:
|
[Lo1] LOUBOUTIN S.-OKAZAKI R.: Determination of all non-normal quartic $CM$-fields and of all non-abelian normal octic $CM$-fields with class number one.Acta Arith. 67 (1994), 47-62. Zbl 0809.11069, MR 1292520 |
| Reference:
|
[Lo2] LOUBOUTIN S.-OKAZAKI R.: The class number one problem for some nonabelian normal $CM$-fields of 2-power degrees.Proc. London Math. Soc. (3) 76 (1998), 523-548. MR 1616805 |
| Reference:
|
[Lo3] LOUBOUTIN S.-OKAZAKI R.: Determination of all quaternion $CM$-fields with ideal class groups of exponent 2.Osaka J. Math. 36 (1999), 229-257. Zbl 0952.11025, MR 1736479 |
| Reference:
|
[Lou1] LOUBOUTIN S.: Continued fractions and real quadratic fields.J. Number Theory 30 (1988), 167-176. Zbl 0652.12002, MR 0961914 |
| Reference:
|
[Lou2] LOUBOUTIN S.: On the class number one problem for the non-normal quartic $CM$-fields.Tohoku Math. J. (2) 46 (1994), 1-12. MR 1256724 |
| Reference:
|
[Lou3] LOUBOUTIN S.: Calcul du nombre de classes des corps de nombres.Pacific J. Math. 171 (1995), 455-467. Zbl 0854.11060, MR 1372239 |
| Reference:
|
[Lou4] LOUBOUTIN S.: Determination of all nonquadratic imaginary cyclic number fields of 2-power degrees with ideal class groups of exponents $< 2$., Math. Comp. 64 (1995), 323-340. MR 1248972 |
| Reference:
|
[Lou5] LOUBOUTIN S.: The class number one problem for the non-abelian normal $CM$-fields of degre 16.Acta Arith. 82 (1997), 173-196. MR 1477509 |
| Reference:
|
[Lou6] LOUBOUTIN S.: Powerful necessary conditions for class number problems.Math. Nachr. 183 (1997), 173-184. Zbl 0871.11078, MR 1434981 |
| Reference:
|
[Lou7] LOUBOUTIN S.: Hasse unit indices of dihedral octic $CM$-fields.Math. Nachr. 215 (2000), 107-113. Zbl 0972.11105, MR 1768197 |
| Reference:
|
[Lou8] LOUBOUTIN S.: Explicit lower bounds for residues at $s = 1$ of Dedekind zeta functions and relative class numbers of $CM$-fields.Trans. Amer. Math. Soc. 355 (2003), 3079-3098. Zbl 1026.11085, MR 1974676 |
| Reference:
|
[Mor] MORTON P.: On Rédei's theory of the Pell equation.J. Reine Angew. Math. 307/308 (1979), 373-398. Zbl 0395.12018, MR 0534233 |
| Reference:
|
[YK] YANG H.-S.-KWON S.-H.: The non-normal quartic $CM$-fields and the octic dihedral $CM$-fields with relative class number two.J. Number Theory 79 (1999), 175-193. Zbl 0976.11051, MR 1728146 |
| . |
