Let be a finite extension of a global field. Such an extension can be generated over 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 une extension finie d’un corps global, donc contient un élément primitif , c’est à dire . 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.
@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/} }
TY - JOUR TI - Small generators of function fields JO - Journal de Théorie des Nombres de Bordeaux PY - 2010 DA - 2010/// SP - 747 EP - 753 VL - 22 IS - 3 PB - Université Bordeaux 1 UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.744/ UR - https://zbmath.org/?q=an%3A1233.11120 UR - https://www.ams.org/mathscinet-getitem?mr=2769343 UR - https://doi.org/10.5802/jtnb.744 DO - 10.5802/jtnb.744 LA - en ID - JTNB_2010__22_3_747_0 ER -
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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