The kataklysmic event:
In the time between August 1987 and January 1989 I discovered [1] 5 exotic radicands, missing from the listing of 16 radicands D of exotic pure cubic fields Q(D^{1/3}) of principal factorization type BETA on page 273 in the paper [2] of H. C. WILLIAMS.
These radicands are:
1430 | 6370 | 9922 | 11284 | 12673 |
Concepts and details:
A description of the concepts "principal factorization type BETA" resp. "exotic" you will find on the page Principal Factors in Pure Cubic Fields resp. Algorithm of VORONOI in Pure Cubic Fields.
A correct table of all 21 exotic pure cubic fields Q(D^{1/3}) with normalized radicands D < 15000 showing the discriminant d, the radicand D = mn^{2} with its quadratic part n, the Dedekind type, 2 minimal norms of principal factors (if they exist), the period length, the regulator R, and the class number h you get by linking to my database Exotic Pure Cubic Fields. For the most recent results see my series Joint Research 2002.
Bibliography:
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