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

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.

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.

@article{JTNB_2004__16_3_569_0,
     author = {Ennola, Veikko},
     title = {Fundamental units in a family of cubic fields},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux 1},
     volume = {16},
     number = {3},
     year = {2004},
     pages = {569-575},
     doi = {10.5802/jtnb.461},
     mrnumber = {2144958},
     zbl = {1079.11056},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2004__16_3_569_0}
}
Ennola, Veikko. Fundamental units in a family of cubic fields. Journal de théorie des nombres de Bordeaux, Volume 16 (2004) no. 3, pp. 569-575. doi : 10.5802/jtnb.461. http://www.numdam.org/item/JTNB_2004__16_3_569_0/

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