Daniel's Exotic Secret

Mysterious pure cubic fields

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(D1/3) 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(D1/3) with normalized radicands D < 15000 showing the discriminant d, the radicand D = mn2 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.


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