ArticleOriginal scientific text

Title

Construction of the real dihedral number fields of degree 2p. Applications

Authors 1, 2, 1

Affiliations

  1. Département de Mathématiques et Mécanique, Université de Caen, Campus 2, BP 5186, 14032 Caen Cedex, France
  2. Department of Mathematics, Korea University, 136-701 Seoul, Korea

Keywords

dihedral field, dihedral group, CM-field

Bibliography

  1. [Cox] D. A. Cox, Primes of the Form x²+ny², Wiley, 1989.
  2. [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.
  3. [Has] H. Hasse, Arithmetische Theorie der kubischen Zahlkörper auf klassenkörpertheoretischer Grundlage, Math. Z. 31 (1930), 565-582.
  4. [Jan] G. Janusz, Algebraic Number Fields, Academic Press, New York, 1973.
  5. [Lef] Y. Lefeuvre, Corps diédraux à multiplication complexe principaux, preprint, Univ. Caen, 1999, submitted.
  6. [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.
  7. [Lou] S. Louboutin, Computation of relative class numbers of CM-fields by using Hecke L-functions, Math. Comp., to appear.
  8. [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.
  9. [LP] S. Louboutin and Y.-H. Park, Class number problems for dicyclic CM-fields, preprint, Univ. Caen, 1998.
  10. [Mar] J. Martinet, Sur l'arithmétique des extensions à groupe de Galois diédral d'ordre 2p, Ann. Inst. Fourier (Grenoble) 19 (1969), 1-80.
  11. [Por] J. Porusch, Die Arithmetik in Zahlkörpern, deren zugehörige Galoissche Körper spezielle metabelsche Gruppen besitzen, auf klassenkörpertheoretischer Grundlage, Math. Z. 37 (1933), 134-160.
Pages:
201-215
Main language of publication
English
Received
1998-05-05
Accepted
1998-09-29
Published
1999
Exact and natural sciences