Some Methods for Evaluating the Regulator of a Real Quadratic Function Field

@article{Stein1999SomeMF,
  title={Some Methods for Evaluating the Regulator of a Real Quadratic Function Field},
  author={Andreas Stein and Hugh C. Williams},
  journal={Experimental Mathematics},
  year={1999},
  volume={8},
  pages={119-133}
}
We develop methods for the rapid computation of the regulator of a real quadratic congruence function field K = k(x)(√D). By extending Shanks' infrastructure ideas in real quadratic number fields to real quadratic congruence function fields we obtain a baby step–giant step method for evaluating the regulator of K in O(|D|¼) polynomial operations. We also show the existence of an effective algorithm which computes the regulator unconditionally in O(|D|⅕) polynomial operations. By implementing… CONTINUE READING

Topics from this paper.