A262562 - OEIS

%I #10 Jun 23 2020 06:17:09

%S 1,0,0,-4,-6,-1,1,-1,4,3,-3,2,-30,-7,-3,1,1,6,3,-3160,2,-1,0,

%T 103819462,9,54,97392,-24,3,3,-3

%N The y 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, A262563.

%K sign,more

%O 2,4

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