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A Rapid Method of Evaluating the Regulator and Class Number of a Pure Cubic Field

1983
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Mathematics of Computation
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Let % = 2(0) be the algebraic number field formed by adjoining 9 to the rationals 2. Let R and h be, respectively, the regulator and class number of %. Shanks has described a method of evaluating R for 2(vD ), where D is a positive integer. His technique improved the speed of the usual continued fraction algorithm for finding R by allowing one to proceed almost directly from the nth to the mth step, where m is approximately In, in the continued fraction expansion of \¡D . This paper shows how

doi:10.2307/2007780
fatcat:ntuowfkww5aztit7ge3cyaucwu