@article{MASLO_2004_54_5_a9,
author = {Louboutin, St\'ephane and Yang, Hee-Sun and Kwon, Soun-Hi},
title = {The non-normal quartic {CM-fields} and the dihedral octic {CM-fields} with ideal class groups of exponent $\le 2$},
journal = {Mathematica slovaca},
pages = {535--574},
year = {2004},
volume = {54},
number = {5},
mrnumber = {2114623},
zbl = {1108.11085},
language = {en},
url = {http://geodesic.mathdoc.fr/item/MASLO_2004_54_5_a9/}
}
TY - JOUR AU - Louboutin, Stéphane AU - Yang, Hee-Sun AU - Kwon, Soun-Hi TI - The non-normal quartic CM-fields and the dihedral octic CM-fields with ideal class groups of exponent $\le 2$ JO - Mathematica slovaca PY - 2004 SP - 535 EP - 574 VL - 54 IS - 5 UR - http://geodesic.mathdoc.fr/item/MASLO_2004_54_5_a9/ LA - en ID - MASLO_2004_54_5_a9 ER -
%0 Journal Article %A Louboutin, Stéphane %A Yang, Hee-Sun %A Kwon, Soun-Hi %T The non-normal quartic CM-fields and the dihedral octic CM-fields with ideal class groups of exponent $\le 2$ %J Mathematica slovaca %D 2004 %P 535-574 %V 54 %N 5 %U http://geodesic.mathdoc.fr/item/MASLO_2004_54_5_a9/ %G en %F MASLO_2004_54_5_a9
Louboutin, Stéphane; Yang, Hee-Sun; Kwon, Soun-Hi. The non-normal quartic CM-fields and the dihedral octic CM-fields with ideal class groups of exponent $\le 2$. Mathematica slovaca, Tome 54 (2004) no. 5, pp. 535-574. http://geodesic.mathdoc.fr/item/MASLO_2004_54_5_a9/
[Ear] EARNEST A. G.: Exponents of the class groups of imaginary abelian number fields. Bull. Austral. Math. Soc. 35 (1987), 231-245. | MR | Zbl
[Lan1] LANG S.: Cyclotomic Fields I and II. (combined 2nd ed.). Grad. Texts in Math. 121, Springer-Verlag, New York, 1990. | MR | Zbl
[Lan2] LANG S.: Algebraic Number Theory. (2nd ed.). Grad. Texts in Math. 110, Springer-Verlag, New York, 1994. | MR | Zbl
[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. | MR | Zbl
[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
[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. | MR | Zbl
[Lou1] LOUBOUTIN S.: Continued fractions and real quadratic fields. J. Number Theory 30 (1988), 167-176. | MR | Zbl
[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
[Lou3] LOUBOUTIN S.: Calcul du nombre de classes des corps de nombres. Pacific J. Math. 171 (1995), 455-467. | MR | Zbl
[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
[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
[Lou6] LOUBOUTIN S.: Powerful necessary conditions for class number problems. Math. Nachr. 183 (1997), 173-184. | MR | Zbl
[Lou7] LOUBOUTIN S.: Hasse unit indices of dihedral octic $CM$-fields. Math. Nachr. 215 (2000), 107-113. | MR | Zbl
[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. | MR | Zbl
[Mor] MORTON P.: On Rédei's theory of the Pell equation. J. Reine Angew. Math. 307/308 (1979), 373-398. | MR | Zbl
[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. | MR | Zbl