Small generators of function fields
Martin Widmer1
1 Institut für Mathematik A Technische Universität Graz Steyrergasse 30/II 8010 Graz, Austria
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.

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, 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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  • Michael Rosen A geometric proof of Hermite's theorem in function fields, Journal de Théorie des Nombres de Bordeaux, Volume 29 (2017) no. 3, pp. 799-813 | DOI:10.5802/jtnb.1001 | Zbl:1396.11118
  • Siman Wong A field theoretic proof of Hermite's theorem for function fields, Archiv der Mathematik, Volume 105 (2015) no. 4, pp. 351-360 | DOI:10.1007/s00013-015-0818-6 | Zbl:1327.11083
  • Jeffrey D. Vaaler; Martin Widmer A note on generators of number fields, Diophantine methods, lattices, and arithmetic theory of quadratic forms. Proceedings of the international workshop, Banff International Research Station (BIRS), Alberta, Canada, November 13–18, 2011, Providence, RI: American Mathematical Society (AMS), 2013, pp. 201-211 | Zbl:1307.11108

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