@article{COMIM_2002_10_1_a0,
author = {Boutteaux, G\'erard and Louboutin, St\'ephane},
title = {The class number one problem for the non-normal sextic {CM-fields.} {Part} 2},
journal = {Communications in Mathematics},
pages = {3--23},
year = {2002},
volume = {10},
number = {1},
mrnumber = {1943019},
zbl = {1042.11070},
language = {en},
url = {http://geodesic.mathdoc.fr/item/COMIM_2002_10_1_a0/}
}
TY - JOUR AU - Boutteaux, Gérard AU - Louboutin, Stéphane TI - The class number one problem for the non-normal sextic CM-fields. Part 2 JO - Communications in Mathematics PY - 2002 SP - 3 EP - 23 VL - 10 IS - 1 UR - http://geodesic.mathdoc.fr/item/COMIM_2002_10_1_a0/ LA - en ID - COMIM_2002_10_1_a0 ER -
Boutteaux, Gérard; Louboutin, Stéphane. The class number one problem for the non-normal sextic CM-fields. Part 2. Communications in Mathematics, Tome 10 (2002) no. 1, pp. 3-23. http://geodesic.mathdoc.fr/item/COMIM_2002_10_1_a0/
[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. | DOI | MR
[Bou] G. Boutteaux. : Détermination des corps à multiplication complexe, sextiques, non galoisiens et principaux. PҺD Thesis, in preparation.
[Lan] S. Lang. : Algebraic Number Theory. Spгinger-Verlag, Grad. Texts Math. 110, Second Edition. | MR | Zbl
[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. | DOI | MR
[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
[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. | DOI | MR
[Loul] S. Louboutin. : On the class number one problem for nonnormal quartic CM-fields. Tôhoku Math. J. 46 (1994), 1-12. | DOI | MR
[Lou2] S. Louboutin. : Lower bounds for relative class numbers of CM-fields. Proc. Amer. Math. Soc. 120 (1994), 425-434. | DOI | MR | Zbl
[LouЗ] S. Louboutin. : Determination of all quaternion octic CM-fields with class number 2. J. London. Math. Soc. (2) 54 (1996), 227-238. | DOI | MR | Zbl
[Lou4] S. Louboutin. : Computation of relative class numbers of CM-fields. Math. Comp. 66 (1997), 173-184. | DOI | MR | Zbl
[Lou5] S. Louboutin. : Upper bounds on $|L(1,\chi)|$ and applications. Canad. J. Math. 50 (1999), 794-815. | DOI | MR | Zbl
[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. | DOI | MR | Zbl
[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. | DOI | MR | Zbl
[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).
[Mar] J. Martinet. : Sur ľarithmétique des extensions à groupe de Galois diédral ďordre 2p. Ann. Inst. Fourier (GrenoЫe) 19 (1969), 1-80. | DOI | MR
[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
[Sta] H. M. Stark. : Some effective cases of the Brauer-Siegel theorem. Invent. Math. 23 (1974), 135-152. | DOI | MR | Zbl
[Wa] L. C. Washington. : Introduction to Cyclotomic Fields. Grad. Texts Math. 83, Springer-Verlag. | MR | Zbl