An improved method of computing the regulator of a real quadratic function field

Abstract

There exists an effective algorithm for computing the regulator of a real quadratic congruence function field K=k(X)(√D) of genus g=deg(D)/2−1 in O(q 2/5g ) polynomial operations. In those cases where the regulator exceeds 108, this algorithm tends to be far better than the Baby step-Giant step algorithm which performs O(q 2/5) polynomial operations. We show how we increased the speed of the O(q 2/5g )-algorithm such that we are able to large values of regulators of real quadratic congruence function fields of small genus.