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The z coordinate of the fundamental unit in the cubic field Q(D^(1/3)): see Comments for precise definition.
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%I #8 Jun 23 2020 06:13:23

%S 0,1,1,2,3,0,0,2,-2,-3,2,-1,12,0,3,-1,-1,4,-4,6230,-4,0,1,370284,-3,

%T 20,-394098,-51,-1,-6,0

%N The z coordinate of the fundamental unit in the cubic field Q(D^(1/3)): see Comments for precise definition.

%C Let D be the n-th cubefree number greater than 1, that is, D = A004709(n), n >= 2.

%C Let F = cubic field Q(D^(1/3)). Let eta be the positive fundamental unit in F. Then eta has a unique representation as eta = x + y*alpha + z*gamma, where (1,alpha,gamma) is the appropriate modified Dedekind basis for F. Then x,y,z are given by A262561, A262562, A262563 respectively.

%C See Sved (1970) for further details. Sved gives a table for all D < 200.

%H Marta Sved, <a href="http://annalesm.elte.hu/annales13-1970/Annales_1970_T-XIII.pdf">Units in pure cubic number fields</a>, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 13 (1970), 141-149.

%Y Cf. A004709, A262561, A262562.

%K sign,more

%O 2,4

%A _N. J. A. Sloane_, Oct 18 2015