Discriminants of Chebyshev radical extensions
Journal de Théorie des Nombres de Bordeaux, Tome 26 (2014) no. 3, pp. 607-633.

Soit t un nombre entier et 2 un nombre premier. Soit Φ(x)=T n (x)-t la composition n-fois du polynôme de Tchebychev de degré décalée de t. Supposant que ce polynôme est irréductible, soit K=(θ), où θ est une racine de Φ. Nous appliquons un théorème de Dedekind en conjonction avec des résultats antérieurs de l’auteur afin d’obtenir des conditions sur t qui assurent que K soit monogène. Pour d’autres valeurs de t, nous appliquons un théorème de Guàrdia, Montes, et Nart pour obtenir une formule pour le discriminant de K et calculons une base intègrale de l’anneau des entiers 𝒪 K .

Let t be any integer and fix an odd prime . Let Φ(x)=T n (x)-t denote the n-fold composition of the Chebyshev polynomial of degree shifted by t. If this polynomial is irreducible, let K=(θ), where θ is a root of Φ. We use a theorem of Dedekind in conjunction with previous results of the author to give conditions on t that ensure K is monogenic. For other values of t, we apply a result of Guàrdia, Montes, and Nart to obtain a formula for the discriminant of K and compute an integral basis for the ring of integers 𝒪 K .

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DOI : https://doi.org/10.5802/jtnb.882
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     title = {Discriminants of {Chebyshev} radical extensions},
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T. Alden Gassert. Discriminants of Chebyshev radical extensions. Journal de Théorie des Nombres de Bordeaux, Tome 26 (2014) no. 3, pp. 607-633. doi : 10.5802/jtnb.882. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.882/

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