Annales Mathématiques
Blaise Pascal
no. 2
A note on the spectrum of a rational function
[Une note sur le spectre d’une fonction rationnelle]
Mohamed Benelmekki1 ; Salah Najib2
1 Université Sultan Moulay Slimane Laboratoire de Mathématiques et Applications, FST Campus Mghilla, BP 523, 23000 Béni Mellal MAROC
2 Université Sultan Moulay Slimane, Faculté Polydisciplinaire de Khouribga Laboratoire multidisciplinaire de recherche et d’innovation BP 145, Hay Ezzaytoune, 25000 Khouribga MAROC
Annales mathématiques Blaise Pascal, Tome 30 (2023) no. 2, pp. 107-114.

En 2008, Bodin a fourni une approche alternative pour borner l’ordre total de réductibilité d’une fonction rationnelle indécomposable. Sa preuve a utilisé certaines propriétés de dérivation jacobienne. Dans cette note, nous revisitons cette preuve et éliminer l’aspect de dérivation jacobienne. Le nouvel ingrédient de notre présentation est une version du théorème de Lüroth.

In 2008, Bodin provided an alternative approach for bounding the total reducibility order of a non-composite rational function. His proof used some properties of jacobian derivation. In this note, we revisit this proof and eliminate the jacobian derivation aspect. The new ingredient in our presentation is a version of Lüroth’s theorem.

Publié le :
DOI : 10.5802/ambp.418
Classification : 12E05, 12F20, 11C08
Mots clés : Irreducible polynomials, Indecomposable rational function, Spectrum of a rational function, Lüroth’s theorem

Mohamed Benelmekki 1 ; Salah Najib 2

1 Université Sultan Moulay Slimane Laboratoire de Mathématiques et Applications, FST Campus Mghilla, BP 523, 23000 Béni Mellal MAROC
2 Université Sultan Moulay Slimane, Faculté Polydisciplinaire de Khouribga Laboratoire multidisciplinaire de recherche et d’innovation BP 145, Hay Ezzaytoune, 25000 Khouribga MAROC
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Mohamed Benelmekki; Salah Najib. A note on the spectrum of a rational function. Annales mathématiques Blaise Pascal, Tome 30 (2023) no. 2, pp. 107-114. doi : 10.5802/ambp.418. https://ambp.centre-mersenne.org/articles/10.5802/ambp.418/

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