Construction of the real dihedral number fields of degree 2p. Applications
Stéphane Louboutin ; Young-Ho Park ; Yann Lefeuvre
Acta Arithmetica, Tome 89 (1999), p. 201-215 / Harvested from The Polish Digital Mathematics Library
Publié le : 1999-01-01
EUDML-ID : urn:eudml:doc:207265
@article{bwmeta1.element.bwnjournal-article-aav89i3p201bwm,
     author = {St\'ephane Louboutin and Young-Ho Park and Yann Lefeuvre},
     title = {Construction of the real dihedral number fields of degree 2p. Applications},
     journal = {Acta Arithmetica},
     volume = {89},
     year = {1999},
     pages = {201-215},
     zbl = {1128.11316},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav89i3p201bwm}
}
Stéphane Louboutin; Young-Ho Park; Yann Lefeuvre. Construction of the real dihedral number fields of degree 2p. Applications. Acta Arithmetica, Tome 89 (1999) pp. 201-215. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav89i3p201bwm/

[000] [Cox] D. A. Cox, Primes of the Form x²+ny², Wiley, 1989. | Zbl 1275.11002

[001] [FQ] A. Fröhlich and J. Queyrut, On the functional equation of the Artin L-function for characters of real representations, Invent. Math. 20 (1973), 125-138. | Zbl 0256.12010

[002] [Has] H. Hasse, Arithmetische Theorie der kubischen Zahlkörper auf klassenkörpertheoretischer Grundlage, Math. Z. 31 (1930), 565-582. | Zbl 56.0167.02

[003] [Jan] G. Janusz, Algebraic Number Fields, Academic Press, New York, 1973.

[004] [Lef] Y. Lefeuvre, Corps diédraux à multiplication complexe principaux, preprint, Univ. Caen, 1999, submitted.

[005] [LL] Y. Lefeuvre and S. Louboutin, The class number one problem for the dihedral CM-fields, in: Proc. ICM 1998 satellite conference, Algebraic Number Theory and Diophantine Analysis, Graz. | Zbl 0958.11071

[006] [Lou] S. Louboutin, Computation of relative class numbers of CM-fields by using Hecke L-functions, Math. Comp., to appear. | Zbl 0931.11050

[007] [LOO] S. Louboutin, R. Okazaki and M. Olivier, The class number one problem for some non-abelian normal CM-fields, Trans. Amer. Math. Soc. 349 (1997), 3657-3678. | Zbl 0893.11045

[008] [LP] S. Louboutin and Y.-H. Park, Class number problems for dicyclic CM-fields, preprint, Univ. Caen, 1998. | Zbl 0963.11065

[009] [Mar] J. Martinet, Sur l'arithmétique des extensions à groupe de Galois diédral d'ordre 2p, Ann. Inst. Fourier (Grenoble) 19 (1969), 1-80. | Zbl 0165.06502

[010] [Por] J. Porusch, Die Arithmetik in Zahlkörpern, deren zugehörige Galoissche Körper spezielle metabelsche Gruppen besitzen, auf klassenkörpertheoretischer Grundlage, Math. Z. 37 (1933), 134-160. | Zbl 59.0945.02