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

Stéphane Louboutin; Young-Ho Park; Yann Lefeuvre

Acta Arithmetica (1999)

  • Volume: 89, Issue: 3, page 201-215
  • ISSN: 0065-1036

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Stéphane Louboutin, Young-Ho Park, and Yann Lefeuvre. "Construction of the real dihedral number fields of degree 2p. Applications." Acta Arithmetica 89.3 (1999): 201-215. <http://eudml.org/doc/207265>.

@article{StéphaneLouboutin1999,
author = {Stéphane Louboutin, Young-Ho Park, Yann Lefeuvre},
journal = {Acta Arithmetica},
keywords = {dihedral field; dihedral group; CM-field},
language = {eng},
number = {3},
pages = {201-215},
title = {Construction of the real dihedral number fields of degree 2p. Applications},
url = {http://eudml.org/doc/207265},
volume = {89},
year = {1999},
}

TY - JOUR
AU - Stéphane Louboutin
AU - Young-Ho Park
AU - Yann Lefeuvre
TI - Construction of the real dihedral number fields of degree 2p. Applications
JO - Acta Arithmetica
PY - 1999
VL - 89
IS - 3
SP - 201
EP - 215
LA - eng
KW - dihedral field; dihedral group; CM-field
UR - http://eudml.org/doc/207265
ER -

References

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  1. [Cox] D. A. Cox, Primes of the Form x²+ny², Wiley, 1989. Zbl1275.11002
  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. Zbl0256.12010
  3. [Has] H. Hasse, Arithmetische Theorie der kubischen Zahlkörper auf klassenkörpertheoretischer Grundlage, Math. Z. 31 (1930), 565-582. Zbl56.0167.02
  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. Zbl0958.11071
  7. [Lou] S. Louboutin, Computation of relative class numbers of CM-fields by using Hecke L-functions, Math. Comp., to appear. Zbl0931.11050
  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. Zbl0893.11045
  9. [LP] S. Louboutin and Y.-H. Park, Class number problems for dicyclic CM-fields, preprint, Univ. Caen, 1998. Zbl0963.11065
  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. Zbl0165.06502
  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. Zbl59.0945.02

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