On montre qu’un entier algébrique cubique sur un corps de nombres de trace nulle est la différence de deux conjugués sur d’un entier algébrique. On prouve aussi que si est une extension cubique normale du corps des rationnels, alors tout entier de de trace zéro est la différence de deux conjugués d’un entier de si et seulement si la valuation adique du discriminant de est différente de .
We show that a cubic algebraic integer over a number field with zero trace is a difference of two conjugates over of an algebraic integer. We also prove that if is a normal cubic extension of the field of rational numbers, then every integer of with zero trace is a difference of two conjugates of an integer of if and only if the adic valuation of the discriminant of is not
@article{JTNB_2005__17_3_949_0, author = {Toufik Zaimi}, title = {The cubics which are differences of two conjugates of an algebraic integer}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {949--953}, publisher = {Universit\'e Bordeaux 1}, volume = {17}, number = {3}, year = {2005}, doi = {10.5802/jtnb.529}, mrnumber = {2212134}, zbl = {05016596}, language = {en}, url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.529/} }
TY - JOUR AU - Toufik Zaimi TI - The cubics which are differences of two conjugates of an algebraic integer JO - Journal de théorie des nombres de Bordeaux PY - 2005 SP - 949 EP - 953 VL - 17 IS - 3 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.529/ DO - 10.5802/jtnb.529 LA - en ID - JTNB_2005__17_3_949_0 ER -
%0 Journal Article %A Toufik Zaimi %T The cubics which are differences of two conjugates of an algebraic integer %J Journal de théorie des nombres de Bordeaux %D 2005 %P 949-953 %V 17 %N 3 %I Université Bordeaux 1 %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.529/ %R 10.5802/jtnb.529 %G en %F JTNB_2005__17_3_949_0
Toufik Zaimi. The cubics which are differences of two conjugates of an algebraic integer. Journal de théorie des nombres de Bordeaux, Tome 17 (2005) no. 3, pp. 949-953. doi : 10.5802/jtnb.529. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.529/
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