Small generators of the ideal class group

  title={Small generators of the ideal class group},
  author={Karim Belabas and Francisco Diaz y Diaz and Eduardo Friedman},
  journal={Math. Comput.},
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 However, once C K has been computed, one notices that this bound could have been replaced by a much smaller value, and so much work could have been saved… CONTINUE READING

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