A computational technique for determining the class number of a pure cubic field

Pierre Barrucand, H. C. Williams, L. Baniuk
1976 Mathematics of Computation  
Two different computational techniques for determining the class number of a pure cubic field are discussed. These techniques were implemented on an IBM/370-158 computer, and the class number for each pure cubic field Q(D ' ) for D = 2, 3.9999 was obtained. Several tables are presented which summarize the results of these computations. Some theorems concerning the class group structure of pure cubic fields are also given. The paper closes with some conjectures which were inspired by the
more » ... ired by the computer results. Here a(/) = 2d^p{d)F{jld), where F{n) is the number of distinct ideals of norm « in K. Also, CRh = <Í>{1), where h is the class number, R is the regulator and C is a constant. If A < 0, C = 2zr/\/IA| and R = loge" where e, Ç> 1) is the fundamental unit oîK.
doi:10.1090/s0025-5718-1976-0392913-9 fatcat:qr7j43h6kngejmzmsnuoa5b7ru