Computation of the Ideal Class Group of Certain Complex Quartic Fields. II

Richard B. Lakein
1975 Mathematics of Computation  
For quartic fields K = F3(sJtt), where F3 = Q(p) and n = 1 mod 4 is a prime of F3, the ideal class group is calculated by the same method used previously for quadratic extensions of F^ = Q(i), but using Hurwitz' complex continued fraction over Q(p). The class number was found for 10000 such fields, and the previous computation over F. was extended to 10000 cases. The distribution of class numbers is the same for 10000 fields of each type: real quadratic, quadratic over Fj, quadratic over F3.
more » ... adratic over F3. Many fields were found with noncyclic class group, including the first known real quadratics with groups 5X5 and 7X7. Further properties of the continued fractions are also discussed.
doi:10.2307/2005470 fatcat:44z5ridiabeaxatwfntwsnbzce