Improving the Speed of Calculating the Regulator of Certain Pure Cubic Fields
نویسنده
چکیده
3/— Abstract. To calculate R, the regulator of a pure cubic field Q(\Jd), a complete period of Voronoi's continued fraction algorithm over Q(\JD) is usually generated. In this paper it is shown how, in certain pure cubic fields, R can be determined by generating only about one third of this period. These results were used on a computer to find R and 3 — then the class number for all pure cubic fields Q(\Jp), where p is a prime, p= — l (mod 3), and p < 2 x 10 . Graphs illustrating the distribution of such cubic fields with class number one are presented.
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