Small generators of function fields
Journal de Théorie des Nombres de Bordeaux, Volume 22 (2010) no. 3, pp. 747-753.

Let 𝕂/k be a finite extension of a global field. Such an extension can be generated over k by a single element. The aim of this article is to prove the existence of a ”small” generator in the function field case. This answers the function field version of a question of Ruppert on small generators of number fields.

Soit 𝕂/k une extension finie d’un corps global, donc 𝕂 contient un élément primitif α, c’est à dire 𝕂=k(α). Dans cet article, nous démontrons l’existence d’un élément primitif de petite hauteur dans le cas d’un corps de fonctions. Notre résultat est la réponse pour les corps de fonctions à une question de Ruppert sur les petits générateurs des corps de nombres.

Received:
Published online:
DOI: 10.5802/jtnb.744
Martin Widmer 1

1 Institut für Mathematik A Technische Universität Graz Steyrergasse 30/II 8010 Graz, Austria
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Martin Widmer. Small generators of function fields. Journal de Théorie des Nombres de Bordeaux, Volume 22 (2010) no. 3, pp. 747-753. doi : 10.5802/jtnb.744. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.744/

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