Small generators of the ideal class group

@article{Belabas2008SmallGO,
  title={Small generators of the ideal class group},
  author={Karim Belabas and Francisco Diaz y Diaz and Eduardo Friedman},
  journal={Math. Comput.},
  year={2008},
  volume={77},
  pages={1185-1197}
}
Assuming the Generalized Riemann Hypothesis, Bach has shown that the ideal class group C K of a number field K can be generated by the prime ideals of K having norm smaller than 12 ( log |Discriminant(K)| )2 . This result is essential for the computation of the class group and units of K by Buchmann’s algorithm, currently the fastest known. However, once C K has been computed, one notices that this bound could have been replaced by a much smaller value, and so much work could have been saved… CONTINUE READING

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Referenced Papers

Publications referenced by this paper.
Showing 1-9 of 9 references

Sur les petits discriminants, Séminaire Delange-Pisot-Poitou (Théorie des Nombres

  • G. Poitou
  • 2007

Algebraic Number Theory, second ed

  • S. Lang
  • Graduate Texts in Mathematics,
  • 1994

Improved approximations for Euler products, in Number Theory (Halifax, NS

  • E. Bach
  • Amer. Math. Soc.,
  • 1994

On the magnitude of the least prime primitive root

  • L. Murata
  • J. Number Theory
  • 1991

Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung

  • R. Zimmert
  • Invent. Math
  • 1981

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