Cubic polynomials defining monogenic fields with the same discriminant
Davis, Chad T.1 ; Spearman, Blair K. ; Yoo, Jeewon2
1 3333 University Way University of British Columbia - Okanagan Kelowna, BC, Canada, V1V 1V7.
2 3333 University Way University of British Columbia - Okanagan Kelowna, BC, Canada, V1V 1V7
Journal de théorie des nombres de Bordeaux, Tome 30 (2018) no. 3, pp. 991-996.

Un corps de nombres K est dit monogène si son anneau des entiers vérifie 𝒪K=ℤ[θ] pour un certain θ∈𝒪K. La monogénéité d’un corps de nombres n’est pas toujours assurée. En outre, il est rare que deux corps de nombres aient le même discriminant. Donc, trouver des corps avec ces deux propriétés est un problème intéressant. Dans cet article, nous montrons qu’il existe une infinité de triplets de polynômes définissant des corps cubiques monogènes distincts de même discriminant.

Let K be a number field with ring of integers 𝒪K. K is said to be monogenic if 𝒪K=ℤ[θ] for some θ∈𝒪K. Monogeneity of a number field is not always guaranteed. Furthermore, it is rare for two number fields to have the same discriminant, thus finding fields with these two properties is an interesting problem. In this paper we show that there exist infinitely many triples of polynomials defining distinct monogenic cubic fields with the same discriminant.

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DOI : 10.5802/jtnb.1061
Classification : 11R16, 11R29
Mots-clés : Cubic field, monogenic, discriminant
Davis, Chad T. 1 ; Spearman, Blair K.  ; Yoo, Jeewon 2

1 3333 University Way University of British Columbia - Okanagan Kelowna, BC, Canada, V1V 1V7.
2 3333 University Way University of British Columbia - Okanagan Kelowna, BC, Canada, V1V 1V7 
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Davis, Chad T.; Spearman, Blair K.; Yoo, Jeewon. Cubic polynomials defining monogenic fields with the same discriminant. Journal de théorie des nombres de Bordeaux, Tome 30 (2018) no. 3, pp. 991-996. doi : 10.5802/jtnb.1061. https://www.numdam.org/articles/10.5802/jtnb.1061/

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