A Table of Complex Cubic Fields

A Table of Totally Real Cubic Fields

“…The table complements the author's existing table of the 3169 complex nonconjugate cubic fields with discriminants greater than -20,000 (Angelí [1], and Shanks [8]). It has been deposited with the Mathematics of Computation's Depository of Unpublished Mathematical Tables; copies may also be obtained from the author on request.…”

Multiplicities of dihedral discriminants

“…As D. Shanks pointed out in his review [13] of [1], the convergence of these approximations to the asymptotic limits would be rather slow, because the really high multiplicities, which contribute the essential part to the limit, unfortunately occur in very high ranges of discriminants.…”

“…As an application, the minimal occurrences of some higher multiplicities of pure cubic discriminants are determined. The first three cases appear in tables of complex cubic fields [1,5,12] which are ordered by discriminants. The further ones are constructed by means of Theorem 2.1, taking the smallest possible prime factors.…”

“…It might be of interest to list explicitly the root discriminants \dL\2l{ß~X) for the few encountered (p -X )-tuplets of dihedral fields with two prime divisors of the conductor /, if p = 5, 7 (for p = 3, they start with the well-known 1836 [1]). Here, the authors of [5] announce the value «3(2, IO6) = 1 762 instead of 1 683.…”

A Computational Technique for Determining the Class Number of a Pure Cubic Field

“…Other tables of class numbers have been calculated by hand by Cassels [5] and Selmer [14]. It should also be mentioned that Angelí [1] has recently given a list of class numbers for all cubic fields with negative discriminant greater than -20, 000.…”