Effective bounds for the zeros of linear recurrences in function fields
Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 3, pp. 749-766.

Dans cet article, on utilise la généralisation de l’inégalité de Mason (due à Brownawell et Masser [8]) afin d’exhiber des bornes supérieures effectives pour les zéros d’une suite linéaire récurrente définie sur un corps de fonctions à une variable.

De plus, on étudie de problèmes similairs dans ce contexte, comme l’équation G n (x)=G m (P(x)),(m,n) 2 , où (G n (x)) est une suite récurrente de polynômes et P(x) un polynôme fixé. Ce problème a été étudié auparavant dans [14,15,16,17,32].

In this paper, we use the generalisation of Mason’s inequality due to Brownawell and Masser (cf. [8]) to prove effective upper bounds for the zeros of a linear recurring sequence defined over a field of functions in one variable.

Moreover, we study similar problems in this context as the equation G n (x)=G m (P(x)),(m,n) 2 , where (G n (x)) is a linear recurring sequence of polynomials and P(x) is a fixed polynomial. This problem was studied earlier in [14,15,16,17,32].

@article{JTNB_2005__17_3_749_0,
     author = {Clemens Fuchs and Attila Peth\H o},
     title = {Effective bounds for the zeros of linear recurrences in function fields},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {749--766},
     publisher = {Universit\'e Bordeaux 1},
     volume = {17},
     number = {3},
     year = {2005},
     doi = {10.5802/jtnb.518},
     zbl = {05016585},
     mrnumber = {2212123},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.518/}
}
Clemens Fuchs; Attila Pethő. Effective bounds for the zeros of linear recurrences in function fields. Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 3, pp. 749-766. doi : 10.5802/jtnb.518. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.518/

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