Fundamental units in a family of cubic fields
Journal de théorie des nombres de Bordeaux, Tome 16 (2004) no. 3, pp. 569-575.

Soit 𝒪 l’ordre maximal du corps cubique engendré par une racine ε de l’equation x 3 +(-1)x 2 -x-1=0, où , 3. Nous prouvons que ε,ε-1 forment un système fondamental d’unités dans 𝒪, si [𝒪:[ε]]/3.

Let 𝒪 be the maximal order of the cubic field generated by a zero ε of x 3 +(-1)x 2 -x-1 for , 3. We prove that ε,ε-1 is a fundamental pair of units for 𝒪, if [𝒪:[ε]]/3.

DOI : 10.5802/jtnb.461
Ennola, Veikko 1

1 Department of Mathematics University of Turku FIN-20014, Finland
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Ennola, Veikko. Fundamental units in a family of cubic fields. Journal de théorie des nombres de Bordeaux, Tome 16 (2004) no. 3, pp. 569-575. doi : 10.5802/jtnb.461. http://www.numdam.org/articles/10.5802/jtnb.461/

[1] B. N. Delone, D. K. Faddeev, The Theory of Irrationalities of the Third Degree. Trudy Mat. Inst. Steklov, vol. 11 (1940); English transl., Transl. Math. Monographs, vol. 10, Amer. Math. Soc., Providence, R. I., Second printing 1978. | MR | Zbl

[2] V. Ennola, Cubic number fields with exceptional units. Computational Number Theory (A. Pethö et al., eds.), de Gruyter, Berlin, 1991, pp. 103–128. | MR | Zbl

[3] H. G. Grundman, Systems of fundamental units in cubic orders. J. Number Theory 50 (1995), 119–127. | MR | Zbl

[4] M. Mignotte, N. Tzanakis, On a family of cubics. J. Number Theory 39 (1991), 41–49, Corrigendum and addendum, 41 (1992), 128. | MR | Zbl

[5] E. Thomas, Fundamental units for orders in certain cubic number fields. J. Reine Angew. Math. 310 (1979), 33–55. | MR | Zbl

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