| Title:
|
The class number one problem for the non-normal sextic CM-fields. Part 2 (English) |
| Author:
|
Boutteaux, Gérard |
| Author:
|
Louboutin, Stéphane |
| Language:
|
English |
| Journal:
|
Acta Mathematica et Informatica Universitatis Ostraviensis |
| ISSN:
|
1211-4774 |
| Volume:
|
10 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
3-23 |
| . |
| Category:
|
math |
| . |
| MSC:
|
11R21 |
| MSC:
|
11R29 |
| MSC:
|
11R42 |
| MSC:
|
11Y40 |
| idZBL:
|
Zbl 1042.11070 |
| idMR:
|
MR1943019 |
| . |
| Date available:
|
2009-01-30T09:09:08Z |
| Last updated:
|
2013-10-22 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/120573 |
| . |
| Reference:
|
[BL] G. Boutteaux, S. Louboutin. : The ciass number one problem for some non-normal sextic CM-fields.Analytic number theory (Beijing/Kjoto, 1999), 27-37, Dev. Math. 6, Kluwer Acad. Publ., Dordrecht, 2002. MR 1901973, 10.1007/978-1-4757-3621-2_3 |
| Reference:
|
[Bou] G. Boutteaux. : Détermination des corps à multiplication complexe, sextiques, non galoisiens et principaux.PҺD Thesis, in preparation. |
| Reference:
|
[Lan] S. Lang. : Algebraic Number Theory.Spгinger-Verlag, Grad. Texts Math. 110, Second Edition. Zbl 1151.11302, MR 1282723 |
| Reference:
|
[LLO] F. Lemmermeyer S. Louboutin, R. Okazaki. : The class number one problem for some non-abelian normal CM-fields of degree 24.Journal de Théorie des Nombres de Bordeaux 11 (1999), 387-406. MR 1745886, 10.5802/jtnb.257 |
| Reference:
|
[LO] S. Louboutin, R. Okazaki. : Determination of all non-normal quartic CM-fieids and of all non-abelian normal octic CM-fields with class number one.Acta Arith. 67 (1994), 47-62. MR 1292520 |
| Reference:
|
[LOO] S. Louboutin R. Okazaki, M. Olivier. : The class number one probiem for some non-abeiian normal CM-fields.Trans. Amer. Math. Soc. 349 (1997), 3657-3678. MR 1390044, 10.1090/S0002-9947-97-01768-6 |
| Reference:
|
[Loul] S. Louboutin. : On the class number one problem for nonnormal quartic CM-fields.Tôhoku Math. J. 46 (1994), 1-12. MR 1256724, 10.2748/tmj/1178225798 |
| Reference:
|
[Lou2] S. Louboutin. : Lower bounds for relative class numbers of CM-fields.Proc. Amer. Math. Soc. 120 (1994), 425-434. Zbl 0795.11058, MR 1169041, 10.1090/S0002-9939-1994-1169041-0 |
| Reference:
|
[LouЗ] S. Louboutin. : Determination of all quaternion octic CM-fields with class number 2.J. London. Math. Soc. (2) 54 (1996), 227-238. Zbl 0861.11064, MR 1405052, 10.1112/jlms/54.2.227 |
| Reference:
|
[Lou4] S. Louboutin. : Computation of relative class numbers of CM-fields.Math. Comp. 66 (1997), 173-184. Zbl 0879.11064, MR 1422790, 10.1090/S0025-5718-97-00863-6 |
| Reference:
|
[Lou5] S. Louboutin. : Upper bounds on $|L(1,\chi)|$ and applications.Canad. J. Math. 50 (1999), 794-815. Zbl 1209.65156, MR 1638619, 10.4153/CJM-1998-042-2 |
| Reference:
|
[Lou6] S. Louboutin. : Explicit bounds for residues of Dedekind zeta functions, values of L-functions at s = 1, and relative class numbers.J. Number Theory 85 (2000), 263-282. Zbl 0967.11049, MR 1802716, 10.1006/jnth.2000.2545 |
| Reference:
|
[Lou7] S. Louboutin. : Explicit upper bounds for residues of Dedekind zeta functions and values of L-functions at s = 1, and explicit lower bounds for relative class numbers of CM-fields.Canad. J. Math. 53 (2001), 1194-1222. Zbl 0998.11066, MR 1863848, 10.4153/CJM-2001-045-5 |
| Reference:
|
[LYK] S. Louboutin Y.-S. Yang, S.-H. Kwon. : The non-normal quartic CM-fields and the dihedral octic CM-fields with ideal class groups of exponent $\leq 2$.Preprint (2000). |
| Reference:
|
[Mar] J. Martinet. : Sur ľarithmétique des extensions à groupe de Galois diédral ďordre 2p.Ann. Inst. Fourier (GrenoЫe) 19 (1969), 1-80. MR 0262210, 10.5802/aif.307 |
| Reference:
|
[Oka] R. Okazaki. : Non-normal class number one problem and the least prime power-гesidue.In Number Theory and Applications (series: Develoments in Mathematics Volume 2), edited by S. Kanemitsu and K. Györy from Kluwer Academic Publishers (1999) pp. 273-289. MR 1738823 |
| Reference:
|
[Sta] H. M. Stark. : Some effective cases of the Brauer-Siegel theorem.Invent. Math. 23 (1974), 135-152. Zbl 0278.12005, MR 0342472, 10.1007/BF01405166 |
| Reference:
|
[Wa] L. C. Washington. : Introduction to Cyclotomic Fields.Grad. Texts Math. 83, Springer-Verlag. Zbl 0966.11047, MR 1421575 |
| . |
