Computation of Real Quadratic Fields with Class Number One
نویسندگان
چکیده
A rapid method for determining whether the real quadratic field Sí = S(\/D) has class number one is described. The method makes use of the infrastructure idea of Shanks to determine the regulator of .W and then uses the Generalized Riemann Hypothesis to rapidly estimate L(l, x) to the accuracy needed for determining whether or not the class number of 3£ is one. The results of running this algorithm on a computer for all prime values of D up to 109 are also presented, together with further results on runs on intervals of size 107 starting at 10! (t = 9,10,..., 16).
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تاریخ انتشار 2010