Determination of all non-normal quartic CM-fields and of all non-abelian normal octic CM-fields with class number one

Stéphane Louboutin; Ryotaro Okazaki

Acta Arithmetica (1994)

  • Volume: 67, Issue: 1, page 47-62
  • ISSN: 0065-1036

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Stéphane Louboutin, and Ryotaro Okazaki. "Determination of all non-normal quartic CM-fields and of all non-abelian normal octic CM-fields with class number one." Acta Arithmetica 67.1 (1994): 47-62. <http://eudml.org/doc/206617>.

@article{StéphaneLouboutin1994,
author = {Stéphane Louboutin, Ryotaro Okazaki},
journal = {Acta Arithmetica},
keywords = {non-normal quartic CM-fields; relative class number one; class number one; non-abelian normal octic CM-fields},
language = {eng},
number = {1},
pages = {47-62},
title = {Determination of all non-normal quartic CM-fields and of all non-abelian normal octic CM-fields with class number one},
url = {http://eudml.org/doc/206617},
volume = {67},
year = {1994},
}

TY - JOUR
AU - Stéphane Louboutin
AU - Ryotaro Okazaki
TI - Determination of all non-normal quartic CM-fields and of all non-abelian normal octic CM-fields with class number one
JO - Acta Arithmetica
PY - 1994
VL - 67
IS - 1
SP - 47
EP - 62
LA - eng
KW - non-normal quartic CM-fields; relative class number one; class number one; non-abelian normal octic CM-fields
UR - http://eudml.org/doc/206617
ER -

References

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  1. [H] J. Hoffstein, Some analytic bounds for zeta functions and class numbers, Invent. Math. 55 (1979), 37-47. Zbl0474.12009
  2. [Kub] T. Kubota, Über die Beziehung der Klassenzahlen der Unterkörper des bizyklischen biquadratischen Zahlkörper, Nagoya Math. J. 6 (1953), 119-127. Zbl0053.21902
  3. [Lou 1] S. Louboutin, On the class number one problem for non-normal quartic CM-fields, Tôhoku Math. J., to appear. 
  4. [Lou 2] S. Louboutin, Calcul du nombre de classes des corps de nombres, preprint, 1992. 
  5. [Lou 3] S. Louboutin, Calcul des nombres de classes relatifs. Application aux corps octiques quaternioniques à multiplication complexe, C. R. Acad. Sci. Paris Sér. I 317 (1993), 643-646. 
  6. [Lou 4] S. Louboutin, Determination of all quaternion octic CM-fields with class number 2, preprint, 1993. 
  7. [O] A. M. Odlyzko, Some analytic estimates of class numbers and discriminants, Invent. Math. 29 (1975), 275-286. Zbl0299.12010
  8. [Ok] R. Okazaki, On evaluation of L-functions over real quadratic fields, J. Math. Kyoto Univ. 31 (1991), 1125-1153. Zbl0776.11071
  9. [Se] J. P. Serre, Corps Locaux, Hermann, 1968. 
  10. [W] L. C. Washington, Introduction to Cyclotomic Fields, Graduate Texts in Math. 83, Springer, 1982. 
  11. [Y] K. Yamamura, The determination of the imaginary abelian number fields with class number one, Math. Comp., to appear. Zbl0749.11048

Citations in EuDML Documents

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  1. Stéphane Louboutin, The class number one problem for the non-abelian normal CM-fields of degree 16
  2. Gérard Boutteaux, Stéphane Louboutin, The class number one problem for the non-normal sextic CM-fields. Part 2
  3. Ken Yamamura, Maximal unramified extensions of imaginary quadratic number fields of small conductors, II
  4. Stéphane Louboutin, The class number one problem for the dihedral and dicyclic CM-fields
  5. Franz Lemmermeyer, Unramified quaternion extensions of quadratic number fields
  6. F. Lemmermeyer, S. Louboutin, R. Okazaki, The class number one problem for some non-abelian normal CM-fields of degree 24
  7. Young-Ho Park, Soun-Hi Kwon, Determination of all imaginary abelian sextic number fields with class number ≤ 11
  8. Stéphane Louboutin, Corps quadratiques à corps de classes de Hilbert principaux et à multiplication complexe
  9. Yann Lefeuvre, Corps diédraux à multiplication complexe principaux
  10. Ken Yamamura, Determination of the imaginary normal octic number fields with class number one which are not CM-fields

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