Advertisement

Computing ray class groups, conductors and discriminants

  • H. Cohen
  • F. Diaz y Diaz
  • M. Olivier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1122)

Abstract

We describe the computation of ray class groups of number fields, conductors and discriminants of the corresponding Abelian extensions. As an application we give several number fields with discriminants less than previously known ones.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Coh]
    H. Cohen: A course in computational algebraic number theory, GTM 138, Springer-Verlag, Berlin, Heidelberg, New York (1993).Google Scholar
  2. [Co-Di-Ol]
    H. Cohen, F. Diaz y Diaz and M. Olivier: Computing ray class groups, conductors and discriminants, preprint (1996).Google Scholar
  3. [Da-Po]
    M. Daberkow and M. Pohst: Computations with relative extensions of number fields with an application to the construction of Hilbert class fields, Proc. ISAAC'95 (1995), to appear.Google Scholar
  4. [Leu]
    A. Leutbecher: Euclidean fields having a large Lenstra constant, Ann. Inst. Fourier 35, 2 (1985) 83–106.Google Scholar
  5. [Le-Ni]
    A. Leutbecher and G. Niklasch: On cliques of exceptional units and Lenstra's construction of Euclidean fields, Journées arithmétiques 1987 (E. Wirsing, Ed.), Springer Lecture Notes in Math. 1380 (1989), 150–178.Google Scholar
  6. [Mar]
    J. Martinet: Petits discriminants des corps de nombres, Journées arithmétiques 1980 (J.V. Armitage, Ed.), London Math. Soc. Lecture Notes Ser. 56 (1982), 151–193.Google Scholar
  7. [Odl]
    A. M. Odlyzko: Bounds for discriminants and related estimates for class numbers, regulators and zeros of zeta functions: a survey of recent results, Sém. Th. des Nombres Bordeaux (série 2) 2 (1990), 119–141.Google Scholar
  8. [Po-Za]
    M. Pohst and H. Zassenhaus: Algorithmic algebraic number theory, Encyclopedia of Math. and its Applications, Cambridge University Press, Cambridge (1989).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • H. Cohen
    • 1
  • F. Diaz y Diaz
    • 1
  • M. Olivier
    • 1
  1. 1.Laboratoire A2XUniversité Bordeaux ITalence

Personalised recommendations