Let be the maximal order of the cubic field generated by a zero of for , . We prove that is a fundamental pair of units for , if
Soit l’ordre maximal du corps cubique engendré par une racine de l’equation , où , . Nous prouvons que forment un système fondamental d’unités dans , si
@article{JTNB_2004__16_3_569_0, author = {Veikko Ennola}, title = {Fundamental units in a family of cubic fields}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {569--575}, publisher = {Universit\'e Bordeaux 1}, volume = {16}, number = {3}, year = {2004}, doi = {10.5802/jtnb.461}, mrnumber = {2144958}, zbl = {1079.11056}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.461/} }
TY - JOUR AU - Veikko Ennola TI - Fundamental units in a family of cubic fields JO - Journal de théorie des nombres de Bordeaux PY - 2004 SP - 569 EP - 575 VL - 16 IS - 3 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.461/ DO - 10.5802/jtnb.461 LA - en ID - JTNB_2004__16_3_569_0 ER -
Veikko Ennola. 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. https://jtnb.centre-mersenne.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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