The class number one problem for the dihedral and dicyclic CM-fields

Stéphane Louboutin

Colloquium Mathematicae (1999)

  • Volume: 80, Issue: 2, page 259-265
  • ISSN: 0010-1354

Abstract

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We recall the determination of all the dihedral CM-fields with relative class number one, and prove that dicyclic CM-fields have relative class numbers greater than one.

How to cite

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Louboutin, Stéphane. "The class number one problem for the dihedral and dicyclic CM-fields." Colloquium Mathematicae 80.2 (1999): 259-265. <http://eudml.org/doc/210717>.

@article{Louboutin1999,
abstract = {We recall the determination of all the dihedral CM-fields with relative class number one, and prove that dicyclic CM-fields have relative class numbers greater than one.},
author = {Louboutin, Stéphane},
journal = {Colloquium Mathematicae},
keywords = {relative class number; CM-field; dihedral group; dicyclic group; CM-fields; class number one problems; dihedral fields; dicyclic fields},
language = {eng},
number = {2},
pages = {259-265},
title = {The class number one problem for the dihedral and dicyclic CM-fields},
url = {http://eudml.org/doc/210717},
volume = {80},
year = {1999},
}

TY - JOUR
AU - Louboutin, Stéphane
TI - The class number one problem for the dihedral and dicyclic CM-fields
JO - Colloquium Mathematicae
PY - 1999
VL - 80
IS - 2
SP - 259
EP - 265
AB - We recall the determination of all the dihedral CM-fields with relative class number one, and prove that dicyclic CM-fields have relative class numbers greater than one.
LA - eng
KW - relative class number; CM-field; dihedral group; dicyclic group; CM-fields; class number one problems; dihedral fields; dicyclic fields
UR - http://eudml.org/doc/210717
ER -

References

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  3. [LL] Y. Lefeuvre and S. Louboutin, The class number one problem for the dihedral CM-fields, in: Proc. Conf. on Algebraic Number Theory and Diophantine Analysis, Graz, August-September 1998, to appear. Zbl0958.11071
  4. [LLO] F. Lemmermeyer, S. Louboutin and R. Okazaki, The class number one problem for some non-abelian normal CM-fields of degree 24, J. Théor. Nombres Bordeaux, to appear. Zbl1010.11063
  5. [Lou1] S. Louboutin, Determination of all quaternion octic CM-fields with class number 2, J. London Math. Soc. 54 (1996), 227-238. Zbl0861.11064
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  7. [LO1] S. Louboutin and R. Okazaki, 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. Zbl0809.11069
  8. [LO2] S. Louboutin and R. Okazaki, The class number one problem for some non-abelian normal CM-fields of 2-power degrees, Proc. London Math. Soc. (3) 76 (1998), 523-548. Zbl0891.11054
  9. [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
  10. [Mar] J. Martinet, Sur l'arithmétique des extensions galoisiennes à groupe de Galois diédral d'ordre 2p, Ann. Inst. Fourier (Grenoble) 19 (1969), no. 1, 1-80. Zbl0165.06502
  11. [Odl] A. Odlyzko, Some analytic estimates of class numbers and discriminants, Invent. Math. 29 (1975), 275-286. Zbl0299.12010
  12. [TW] A. D. Thomas and G. V. Wood, Group Tables, Shiva Publ. Kent, 1980. 
  13. [Wa] L. C. Washington, Introduction to Cyclotomic Fields, Grad. Texts in Math. 83, Springer, 1982; 2nd ed., 1997. 
  14. [Yam] K. Yamamura, The determination of the imaginary abelian number fields with class-number one, Math. Comp. 206 (1994), 899-921. Zbl0798.11046

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