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

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.

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.

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DOI : https://doi.org/10.5802/jtnb.744
@article{JTNB_2010__22_3_747_0,
     author = {Martin Widmer},
     title = {Small generators of function fields},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {747--753},
     publisher = {Universit\'e Bordeaux 1},
     volume = {22},
     number = {3},
     year = {2010},
     doi = {10.5802/jtnb.744},
     zbl = {1233.11120},
     mrnumber = {2769343},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.744/}
}
Martin Widmer. Small generators of function fields. Journal de Théorie des Nombres de Bordeaux, Tome 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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